# sin (45° + θ) - cos (45° - θ) is equal to

a. 2cosθ

b. 0

c. 2sinθ

d. 1

**Solution:**

We have to find the value of sin (45° + θ) - cos (45° - θ)

By using the trigonometric ratios of complementary angles,

cos (90° - A) = sin A

cos (45° - θ) = cos (90° - (45° - θ))

= cos(90° - 45° + θ)

= sin(45°+ θ)

sin(45°+ θ) - cos(45°- θ) = sin(45°+ θ) - sin(45°+ θ)

= 0

Therefore, the value of the given expression is 0.

**✦ Try This: **cosec (23° + θ) - sec (67° - θ) is equal to

We have to find the value of cosec (23° + θ) - sec (67° - θ)

By using the trigonometric ratios of complementary angles,

sec (90° - A) = cosec A

Now, sec (67° - θ) = sec(90° - (67° - θ))

= sec(90°- 67° + θ)

= cosec(23° + θ)

So, cosec (23° + θ) - sec (67° - θ) = cosec(23° + θ) - cosec(23° + θ) = 0

Therefore, cosec (23° + θ) - sec (67° - θ) is equal to 0.

**☛ Also Check: **NCERT Solutions for Class 10 Maths Chapter 8

**NCERT Exemplar Class 10 Maths Exercise 8.1 Problem 14**

## sin (45° + θ) - cos (45° - θ) is equal to a. 2cosθ, b. 0, c. 2sinθ, d. 1

**Summary:**

Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle. sin (45° + θ) - cos (45° - θ) is equal to 0

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