Test: Applications of Trigonometric Identities - Class 10 MCQ

# Test: Applications of Trigonometric Identities - Class 10 MCQ

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## 15 Questions MCQ Test Mathematics (Maths) Class 10 - Test: Applications of Trigonometric Identities

Test: Applications of Trigonometric Identities for Class 10 2024 is part of Mathematics (Maths) Class 10 preparation. The Test: Applications of Trigonometric Identities questions and answers have been prepared according to the Class 10 exam syllabus.The Test: Applications of Trigonometric Identities MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Applications of Trigonometric Identities below.
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Test: Applications of Trigonometric Identities - Question 1

### If 7sin2x + 3cos2x = 4 then, secx + cosecx =

Detailed Solution for Test: Applications of Trigonometric Identities - Question 1

7sin2x+3cosx=4
7sin2x+3(1-sin2x)=4
7sin2x+3-3sin2x=4
4sin2x=4-3
4sin2x=1
sin2x=¼
sinx=½
Cosec x=1/sinx=2
Cos x=
Sec x= 1/cos x=
Cosec x + sec x=2+

Test: Applications of Trigonometric Identities - Question 2

### Using the formula cos 2θ = 1-2 sin2θ the value of sin 15° is

Detailed Solution for Test: Applications of Trigonometric Identities - Question 2

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Test: Applications of Trigonometric Identities - Question 3

### If tan θ = 12/5, then  is equal to

Detailed Solution for Test: Applications of Trigonometric Identities - Question 3

tanθ = 12/5

so sinθ = 12/13

so

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

= 25/1 = 25

Test: Applications of Trigonometric Identities - Question 4

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

Detailed Solution for Test: Applications of Trigonometric Identities - Question 4

2cosθ = 1
cosθ = 1/2 ⇒ θ = 60 degrees

Test: Applications of Trigonometric Identities - Question 5

Detailed Solution for Test: Applications of Trigonometric Identities - Question 5

Test: Applications of Trigonometric Identities - Question 6

The square root of  ​

Test: Applications of Trigonometric Identities - Question 7

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

Detailed Solution for Test: Applications of Trigonometric Identities - Question 7

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.

Test: Applications of Trigonometric Identities - Question 8

Test: Applications of Trigonometric Identities - Question 9

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

Detailed Solution for Test: Applications of Trigonometric Identities - Question 9

Identities:
cos(90° - θ) = Sin θ
sin (90° - θ) = Cos θ

= cos θ cos(90° - θ) – sin θ sin (90° - θ)
= cos θ . Sin θ  - sin θ . Cos θ = 0

Test: Applications of Trigonometric Identities - Question 10

tan2A – tan2B can also be written as.

Detailed Solution for Test: Applications of Trigonometric Identities - Question 10

Test: Applications of Trigonometric Identities - Question 11

The value of θ for which 2 cos2θ + sinθ - 2 = 0; 0° < θ < 90° is:​

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Test: Applications of Trigonometric Identities - Question 12

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

Detailed Solution for Test: Applications of Trigonometric Identities - Question 12

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)
2A = 90
A = 45
B = 15

Test: Applications of Trigonometric Identities - Question 13

If a cosθ + b sinθ = 4 and a sinθ – b cosθ = 3, then a2 + b2 is

Test: Applications of Trigonometric Identities - Question 14

If θ is an acute angle and tan θ + cot θ​ = 2, then the value of tan7θ + cot7θ is is

Detailed Solution for Test: Applications of Trigonometric Identities - Question 14

Test: Applications of Trigonometric Identities - Question 15

## Mathematics (Maths) Class 10

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## Mathematics (Maths) Class 10

116 videos|420 docs|77 tests