Question

Prove that (sinA+cosecA) ² + (cosA+secA) ² = 7 + tan²A+cos²A​

Answer 1

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Answer 2

HEY MATE+

HERE IS YOUR ANSWER:

STEP BY STEP EXPLANATION:

TO PROVE :

(sinA +cosecA)^2+(cosA+secA)^2=7+tan^2A+cos^2A

LHS: Sin^2A+cosec^2A+2sinAcosecA+cos^2A+sec^2A+2cosAsecA {(a+b)^2=a^2+b^2+2ab}

=sin^2A+cos^2A+(2sinA×1/sinA)+cosec^2+sec^2+(2cosA×1/cosA)

=1+(2)+cosec^2A+sec^2A+(2)

=5+cosec^2A+sec^2A

=5+cot^2A+1+ tan^A+1

=7+cot^2A+tan^2A=RHS

HENCE PROVED

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