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What is the value of sin 137°sin 43° + cos 43°sin 47° 
1. 1/√2
2. √3/2
3. 0
4. 1

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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 

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