Question

sin^2 A tan A+ cos^2 A cot A+ 2 sin A cosA = tan A+ cot A​

Answer 1

${\huge{\underline{\underline{\rm{Question:-}}}}}$

sin²A.tanA + cos²A.cotA + 2 sinA.cosA = tanA + cotA

${\huge{\underline{\underline{\rm{Answer:-}}}}}$

L.H.S.= sin²A× tanA+ cos²A× cotA+ 2sinA×cosA

= sin³A /cosA + cos³A/sinA + 2sinA× cosA

= [sin⁴ + cos⁴+ 2 sin²A× cos²A ]/sinA× cosA

= [sin²A + cos²A)² /sinA × cosA

= 1/sinA× cosA

= [sin²A + cos²A] /sinA× cosA

since [ 1= sin^2 +cos^2a]

= sin²A /sinA× cosA + cos²A/sinA×cosA

=

tan A+ cot A= R.H.S.

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Answer 2

Answer:

Hope this will helps you