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This mock test of Test: Applications of Trigonometric Identities for Class 10 helps you for every Class 10 entrance exam.
This contains 15 Multiple Choice Questions for Class 10 Test: Applications of Trigonometric Identities (mcq) to study with solutions a complete question bank.
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QUESTION: 1

If 7sin^{2}x + 3cos^{2}x = 4 then, secx + cosecx =

Solution:

7sin^{2}x+3cos^{2 }x=4

7sin^{2}x+3(1-sin^{2}x)=4

7sin^{2}x+3-3sin^{2}x=4

4sin^{2}x=4-3

4sin^{2}x=1

sin^{2}x=¼

sinx=½

Cosec x=1/sinx=2

Cos x=

Sec x= 1/cos x=

Cosec x + sec x=2+

QUESTION: 2

Using the formula cos 2θ = 1-2 sin^{2}θ the value of sin 15° is

Solution:

QUESTION: 3

If tan θ = 12/5, then is equal to

Solution:

tanθ = 12/5

so sinθ = 12/13

so

(1 + 12/13)/(1-12/13)

= 25/1 = 25

QUESTION: 4

When 0°< θ < 90°, and 2 cos θ = 1 the value of θ is

Solution:

2cosθ = 1

cosθ = 1/2 ⇒ θ = 60 degrees

QUESTION: 5

Solution:

Rationalise 1 +sinA

QUESTION: 6

The square root of

Solution:

QUESTION: 7

If tanθ < 0, sinθ < 0, then the terminal arm of the angle lies in the quadrant

Solution:

**The correct option is Option A.**

**If the angle is between 0 to 90 degrees then it will lies in the first quadrant.**

**The **tanθ and sinθ have positive values, hence lies in first quadrant.

QUESTION: 8

Solution:

QUESTION: 9

The value of cos θ cos(90° - θ) – sin θ sin (90° - θ) is:

Solution:

QUESTION: 10

tan^{2}A – tan^{2}B can also be written as.

Solution:

QUESTION: 11

The value of θ for which 2 cos^{2}θ + sinθ - 2 =; 0° < θ __<__ 90° is:

Solution:

QUESTION: 12

If 2 cos(A + B) = 1, and 2 sin(A –B) = 1 then the values of A and B are

Solution:

2 cos(A + B) = 1

cos(A + B) = ½

cos(A + B)=cos 60

A+B=60 …(1)

2 sin(A – B) = 1

sin(A - B)=½

sin(A - B)=sin 30

A-B = 30 …(2)

Adding 1 and 2

2A = 90

A = 45

B = 15

QUESTION: 13

If a cosθ + b sinθ = 4 and a sinθ – b cosθ = 3, then a^{2} + b^{2} is

Solution:

QUESTION: 14

If θ is an acute angle and tan θ + cot θ = 2, then the value of tan^{7}θ + cot^{7}θ is is

Solution:

QUESTION: 15

Solution:

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