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प्रश्न
Select the correct option from the given alternatives :
The value of sin(n + 1) A sin (n + 2) A + cos(n + 1) A cos(n + 2) A is equal to
विकल्प
sin A
cos A
– cos A
sin 2A
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उत्तर
cos A
Explanation:
L.H.S. = sin [(n + 1)A] . sin [(n + 2)A] + cos [(n + 1)A] . cos [(n + 2)A]
= cos [(n + 2)A] . cos [(n + 1)A] + sin [(n + 2)A] . sin [(n + 1)A]
Let (n + 2)A = a and (n + 1)A = b …(i)
∴ L.H.S. = cos a . cos b + sin a . sin b
= cos (a − b)
= cos [(n + 2)A − (n + 1)A] ........[From (i)]
= cos [(n + 2 − n − 1)A]
= cos A
= R.H.S.
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