Question

sin²68° + cos²65° + sin²22° + cos²25° equals
(1) 1
(2) 0
(3) 2
(4) 2(sin²68° + cos²65°)​

Answer 1

Step-by-step explanation:

here remember that,

sin²Φ + cos²Φ = 1 and,

(sin²Φ) = (sinΦ )²

_____________________

sin²68° + cos²65° + sin²22° +cos²25°

= )) (sin 68°)² + (cos65°)² +(sin22°)²

+ (cos 25°)²

=)) ( sin 68 °)² + ( cos 65° )²

+ (cos (90° - 22°))² + (sin (90°- 25°))²

=)) (sin 68°)² + (cos 65° )²

+ (cos 68° )² + (sin 65°)²

= )) sin²68° + cos²65° + cos²68° + sin²65°

=)) sin² 68° + cos² 68° +

cos²65° + sin² 65°

=)) 1 + 1

=)) 2

option (3) 2 is a correct option.