if cos² alpha + cos² beta = 2 Find tan³ alpha + sin^5 beta
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Answer:
Shorya9017Maths AryaBhatta
Step-by-step explanation:
cos alpha / sin alpha = 1/2. , so
sin alpha/ cos alpha = 2
tan alpha = sin alpha / cos alpha.
So tan alpha = 2
1/cos beta = -5/3
cos beta = -3/5
sin beta = √ 1- cos ^2 beta
sin beta = √1-(-3×-3/5×5)
= √1-9/25 = √25-9/25
sin beta = √ 16/25 = 4/5
tan beta = sin beta / cos beta
cos beta = -3/5 , sin beta = 4/5
tan beta =( 4/5 )/ (-3/5)
tan beta =-4/3
tan (alpha+beta) = tan alpha + tan beta / 1-tan alpha× tan beta.
={ 2 + (-4/3)}/1-2×(-4/3)
=(6 -4 /3 ) / 1+(8/3)
= (2/3 ) / 3+8/3
=(2/3) / 11/3
=2/3 × 3/11
tan (alpha + beta ) = 2/11
Hope it may help you ♥
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