Question

যদি(1+sinA)(1+sinB)=(1+sinA)(1-sinB)(1-sinC)​

Answer 1

Answer:

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Step-by-step explanation:

Let (1 + sin a) * (1 + sin b) * (1 + sin c) = k = (1 - sin a) * (1 - sin b) * (1 - sin c)

So, (1 + sin a) * (1 + sin b) * (1 + sin c) = k .............1

and (1 - sin a) * (1 - sin b) * (1 - sin c) = k ......2

Now, multiply equation 1 and equation 2, we get

(1 + sin a) * (1 + sin b) * (1 + sin c) * (1 - sin a) * (1 - sin b) * (1 - sin c) = k

=> (1 - sin2 a) * (1 - sin2 b) * (1 - sin2 c) = k

=> cos2 a * cos2 b * cos2 c = k2

taking square root on both side, we get

=> ± cos a * cos b * cos c = k

So, (1 + sin a) * (1 + sin b) * (1 + sin c) = (1 - sin a) * (1 - sin b) * (1 - sin c) = ±cos a *cos b *cos c