Question

Sin ^2 (64°- theta) + Sin ^2 (26°- theta)

Answer 1

Answer:

The value of sin² ( 64° - θ ) + sin² ( 26° - θ ) is 1.

Step-by-step-explanation:

We have to find the value of sin² ( 64° - θ ) + sin² ( 26° - θ ).

sin² ( 64° - θ ) + sin² ( 26° - θ )

⇒ sin² ( 64° - θ ) + sin² [ ( 90° - 64° ) - θ ]

⇒ sin² ( 64° - θ ) + cos² ( 64° - θ ) - - - [ sin² ( 90° - θ ) = cos² θ ]

⇒ 1 - - - [ sin² θ + cos² θ = 1 ]

∴ The value of sin² ( 64° - θ ) + sin² ( 26° - θ ) is 1.

───────────────────────

Additional Information:

Some Trigonometric Identities:

1. sin θ = cos ( 90° - θ )

2. cos θ = sin ( 90° - θ )

3. tan θ = cot ( 90° - θ )

4. cot θ = tan ( 90° - θ )

5. sec θ = cosec ( 90° - θ )

6. cosec θ = sec ( 90° - θ )

7. sin² θ + cos² θ = 1

8. sec² θ = 1 + tan² θ

9. cosec² θ = 1 + cot² θ