Correct Answer - Option 4 : 1
Concept used:
sin(90° - θ) = cosθ
sin(180° - θ) = sinθ
sin(A + B) = sinA cosB + cosA sinB
Calculation:
Given: sin 137°sin 43° + cos 43°sin 47°
sin 137° = sin(180° - 43°) = sin 43°
sin 43° = sin(90° - 47°) = cos47°
sin 43°cos 47° + cos 43°sin 47
by using; Sin (A + B) = SinA CosB + CosA SinB
⇒ sin 43°cos 47° + cos 43°sin 47° = sin (43° + 47°)
= sin 90°
= 1
∴ sin 43°cos 47° + cos 43°sin 47° = 1
sin (x + y) = sin x cos y + cos x sin y
sin (x – y) = sin x cos y – cos x sin y
cos (x – y) = cos x cos y + sin x sin y
cos (x + y) = cos x cos y - sin x sin y
cos (π/2 + x) = – sin x
sin (π/2 + x) = cos x
cos (π – x) = – cos x
sin (π – x) = sin x