## Kerala Plus One Maths Chapter Wise Previous Questions and Answers Chapter 3 Trigonometric Functions

Question 1.

Solve: Sin 2x – Sin 4x + Sin 6x = 0. [March-2018]

Answer:

Question 2.

In a Δ ABC, prove that

Answer:

Question 3.

The maximum value of the function f(x) = Sin x is

i. 1

ii.

iii.

iv. 2

b. Prove that,

(Sin x + Cos x)^{2} = 1+Sin 2x.

c. Find the maximum value of Sin x + Cos x. [March-2018]

Answer:

a. 1

b. (sin x + cosx)^{2 }= sin^{2}x + cos^{2}x + 2sinx cosx = 1 + sin2x

c. Maximum value of sin 2x = 1

Maximum value of sinx + cosx

Question 4.

Sin 405° = …………..

i.

ii.

iii.

iv. 1

b. Sin lies in the second quadrant. Find the values of Cos x, Sec x, Tan x and Cot x.

c. Solve : Sin 2x – Sin 4x + Sin 6x = 0

OR

a. radian =…………………..degree

i. 210

ii. 300

iii.240

iv. 120

b. Find the value of Tan 75°

c. In any triangle ABC, prove that a Sin (B – C) + b Sin (C-A) + i c Sin (A-B) = 0 [March-2017]

Answer:

c. In any Δ ABC, A+B+C=180 A= 180-(B + C)

Let a sin(B – C) = 2R sin A. sin (B – C)

= 2R [sin {180 – (B + C)} sin (B -C)]

= 2R sin (B + C). sin (B -C)

= 2R (sin^{2}B – sin^{2}C)

||^{ly} bsin(C – A) = 2R (sin^{2}C – sin^{2}A) c sin (A – B) = 2R (sin^{2}A – sin^{2}B)

LHS = 2r [sin^{2}B – sin^{2}C + sin^{2}C – sin ^{2}A + sin^{2}A – sin^{2} B] = 2R(0) = 0 =RHS

Question 5.

a. The degree measure of radians is………….

i. 120°

ii. 102°

iii. 201°

iv. 210°

b. Prov that

c. A lamp post is situated at the middle point M of the side AC of a triangular plot ABC with BC=7 m, C A = 8 m, AB = 9 m. Lamp post subtends an angle 15° at the point B. Determine the height of the lamp post. Answer:

a. 210°

Question 6.

a. Which one of the following values of sin x is incorrect?

a.. 0

b. 1/2

c. 3

d. 1

b. Prove that

c. A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 cm. Find the height of the tree.

OR

a. sin 225° =….

Answer:

a. 3

Question 7.

a.The value of Sin (π – x) is………….

b. Find the principal and general solution of the equation [March-2014 ]

Answer:

Question 8.

a. Prove that

b. Prove that

[March -2013]

Answer:

Question 9.

Prove that

Answer:

Question 10.

Solve sin 2x – sin 4x + sin 6x = 0

Answer:

Question 11.

Prove that cot x cot 2x – cot 2x cot 3x – cot 3x cot x = 1. [February-2013]

Answer:

cotx. cot2x – cot2x cot3x – cot3x cotx = 1

cot3x cotx + cot3x cot2x = cotx cot2x -1

cotx – cot2x – cot2x cot3x – cot3x cotx =1

Question 12.

a. Evaluate

b. If and x is in the third quadrant, find sin x and cos x

[March -2010]

Answer:

Question 13.

Prove that

[March-2012]

Answer:

Question 14.

i. Find the value of

ii. Find the principal and general solutions of the equation [March-2011]

Answer:

Question 15.

Show that (cos x+cos y)^{2} +(sin x+sin y)^{2 }=4cos^{2}

Answer:

LHS = cos^{2}x + 2cosxcosy + cos^{2}y + sin^{2}x +

2sinx siny + sin2y

= 2 + 2 (cosx cosy + sinx siny)

=4cos^{2}

Question 16.

i. Find the degree measure corresponding to radians.(use π=22/7)

ii. If cos=1/2 x lies in the third quadrant, find sin x and tan x. [March – 2010]

Answer:

Question 17.

Prove that

[March-2010]

Answer:

Question 18.

a. Expand cos (x + y) and hence prove cos2x = 1 – 2sin^{2}x.

b. Solve the equation tan^{2}θ+ cot^{2 }θ= 2[September-2010]

Answer:

Question 19.

Show that

Answer:

Question 20.

i.Convert radian into degree measure

ii. Find the value of

iii. Find the general solution of the equation

Answer:

Question 21.

Prove that

[August -2009]

Answer:

Question 22.

a. Convert 22°40′ into radian measure.

b If sin x = and x is an acute angle, find the value of cos 2x.

c. Show that

sin(40° + x) cos(10° + x) – cos(40° + x) sin(10° + x) = [March-2009]

Answer:

Question 23.

If ,then prove that (1+tanx)(1+tany)=2 and hence deduce tan [March – 2009]

Answer:

Question 24.

a. The radian measure of 240° is

(1 radian, radian radian, radian)

b. If sinθ= ,cosφ= where θ and φ both lie in the second quadrant, find the value of sin (θ+φ). [September-2008]

Answer:

Question 25.

a. sin 765°=……………..

(i) 0

(ii) 1/2

(iii)

(iv)

Answer:

a.(iii)

b.

Question 26.

i. Show that sin 105° + cos 105°=

ii. Simplify sin 5x – sin 3x

iii. Find the value of tan 22°30’ [June-2008]

Answer:

i. LHS = sin 105 + cos (90 + 15)

= sin 105 – sin 15 = 2cos 60 sin 45

ii. sin 5x – sin 3x = 2cos 4x sin x

iii. tan 22°30’=

Question 27.

If tan θ= and θ lies in the third quadrant,find sin θ and cos θ [June – 2008]

Answer:

sin θ=,cos θ= .

Question 28.

i.Prove that

ii. Find the domain and range off(x) = cos 2x [February-2008]

Answer:

Question 29.

i. Calculate cos 75° and cos 15° using the values of cos 45 and cos 30

ii. Draw the graph of f (x) = sin 2x [February-2008]

Answer:

Question 30.

i. Which among the following is the value of cos 15.

ii. If A + B = 45°, prove that (1+ tanA) (1 + tanB) = 2

iii. Prove that (cosα+cosβ)^{2} + (sinα+sinβ)^{2 } [september – 2007]

Answer:

ii.

Question 31.

i. If tan x = -4/3 and x lies in the second quadrant, then sin x=—

Answer:

i.

Question 32.

i. The value of cos 70 cos 10+ sin 70 sin 10 is

[ 0, 1, 1/2, cos 80 ]

ii. Prove that tan 3x tan 2x tan x = tan3x – tan 2x – tan x [June-2007]

Answer:

Question 33.

If cosA= and cos B= , where A lies in the second quadrant, B lies in the first quadrant

i. Find sin A, sin B.

ii. Also find sin (A + B), cos (A + B)

iii.Find the value of sin 18° [June-2007]

Answer:

Question 34.

If sin (-θ)= and (-θ)= ,then value of

tan θ is…………..

Answer:

Question 35.

Prove that

Hence find the value of

. Also find the value of tan 75° [February – 2007]

Answer:

Question 36.

i. Find the radian measure corresponding to the degree measure 750°

ii. Prove that [June – 2006]

Answer:

Question 37.

i. Which of the following statement is true? [In the I quadrant sinθ decreases from 1 to 0, In the H qudrant sin θ increases from 0 to 1, In the III quadrant sin θ decreases from 0 to -1, In the IV qudrant sin θ increases from 0 to ∞] [June-2006]

Answer: