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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