Express sin 67° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°

Solution:

We will be using the trigonometric ratios of complementary angles to solve the given question.

cos (90° - θ) = sin θ

Given that: sin 67° + cos 75° ….(i)

Since cos (90° - θ) = sin θ

By using this property in equation (i) we get,

sin 67° + cos 75° = sin (90° - 23°) + cos (90° - 15°)

= cos 23° + sin 15°

Hence, the expression cos 23° + sin 15° has trigonometric ratios of angles between 0° and 45°.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 8

Video Solution:

Express sin 67° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°

Maths NCERT Solutions Class 10 Chapter 8 Exercise 8.3 Question 7

Summary:

sin 67° + cos 75° can be expressed as cos 23° + sin 15° in terms of trigonometric ratios of angles between 0° and 45°.

☛ Related Questions:

• Show that: (i) tan 48° tan 23° tan 42° tan 67° = 1 (ii) cos 38° cos 52° - sin 38° sin 52° = 0.
• If tan 2A = cot (A – 18°), where 2A is an acute angle, find the value of A.
• If tan A = cot B, prove that A + B = 90°.
• If sec 4A = cosec (A – 20°), where 4A is an acute angle, find the value of A.