Test: Multiple Angle Formula - JEE MCQ

# Test: Multiple Angle Formula - JEE MCQ

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## 10 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Test: Multiple Angle Formula

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Test: Multiple Angle Formula - Question 1

### Find the value of  sin θ/3

Detailed Solution for Test: Multiple Angle Formula - Question 1

sin θ/3
Multiply and divide it by '2'
sin2(θ/3*2)  = sin2(θ/6)
As we know that sin2θ = 2sinθcosθ
=> 2 sin(θ/6) cos(θ/6)

Test: Multiple Angle Formula - Question 2

### tan 2x =

Detailed Solution for Test: Multiple Angle Formula - Question 2

tan2x = tan(x+x)
(tanx + tanx)/(1 - tan2x)
= 2tanx/(1 - tan2x)

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Test: Multiple Angle Formula - Question 3

### What is the value of tan 3θ ? if tan θ = 1/2

Detailed Solution for Test: Multiple Angle Formula - Question 3

tan3θ = (3tanθ - tan3θ)/(1 - 3tan2θ)
tan θ = 1/2
= [3(1/2) - (1/2)3]/[1 - 3(1/2)2]
= [3/2 - 1/8]/[1 - 3/4]
= [11/8]/[1/4]
= 11/2

Test: Multiple Angle Formula - Question 4

If cos θ = 1/√5 what is the value of cos 2θ?

Detailed Solution for Test: Multiple Angle Formula - Question 4

cos 2θ = 2cos2θ - 1
= 2(1/√5)2 - 1
= 2/5 - 1
= -3/5

Test: Multiple Angle Formula - Question 5

then the value of cos 2θ is

Detailed Solution for Test: Multiple Angle Formula - Question 5

cos θ = 1/2 (a + 1/a)
⇒ cos 2θ = 2 cos2θ − 1
⇒ cos 2θ = 2 [1/2 (a + 1/a)]2 − 1
⇒ cos 2θ = 2 [1/4 (a2 + 1/a2 + 2)] − 1
⇒ cos 2θ = 1/2 [a2 + 1/a2 + 2] − 1
⇒ cos 2θ = a2/2 + 1/2a2 + 1 − 1
⇒ cos 2θ = 1/2 [a2 + 1/a2]

Test: Multiple Angle Formula - Question 6

Find tan θ/3

Detailed Solution for Test: Multiple Angle Formula - Question 6

Identity

Test: Multiple Angle Formula - Question 7

The value of tan

Detailed Solution for Test: Multiple Angle Formula - Question 7

tan(45°) = tan(45°/2 + 45°/2)
= 2tan(45°/2)/(1 - tan2(45°/2))
(Using expansion for tan(2x))
This implies, 1 = 2tan(45°/2)/(1 - tan2(45°/2))
Rearranging terms, tan2(45°/2) + 2tan(45°/2) - 1 = 0
Solving the quadratic equation x2 + 2x - 1 = 0 gives
x = (√2 - 1) or (-√2 - 1)
But tan(45°/2) lies in the first quadrant, therefore it should be positive.
tan(45°/2) = (√2 - 1)

Test: Multiple Angle Formula - Question 8

When sinθ + cosθ = 1, then the value of sin2θ is

Detailed Solution for Test: Multiple Angle Formula - Question 8

Squaring on both sides,you get sin2x + 2sinxcosx + cos2x = 1

which gives 1 + 2sinxcosx = 1 {since sin2x +cos2x = 1 for all x}

which means,2sinxcosx =0

which means either sinx =0 or cosx=0

so,the general solution is that for sinx=0 union cosx=0

Test: Multiple Angle Formula - Question 9

What is the value of cosθ/2 ?

Detailed Solution for Test: Multiple Angle Formula - Question 9

cos2θ = cos2θ − sin2θ
And: cos2θ + sin2θ=1
we find:
cos2θ=(1−sin2θ)−sin2θ=1−2sin2θ
θ = θ/4
cosθ/2 = 1−2sin2θ/4

Test: Multiple Angle Formula - Question 10

sin x = 1/4 ; the possible values of tan x/2 are

Detailed Solution for Test: Multiple Angle Formula - Question 10

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## Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests