Question

${ \cot(?) }^{2} \alpha ( \sec( \alpha - 1 \div 1 \ + \sin( \alpha ) + { \sec(?) }^{2} \alpha ( \sin( \alpha - 1 \div 1 + \sec( \alpha ) ) )$
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Answer 1

LHS

=cot²A(secA-1)/(1+sinA)

={(cos²A/sin²A)(1/cosA-1)}/(1+sinA)

=[{cos²A/(1-cos²A)}{(1-cosA)/cosA}]/(1+sinA)

=[{cos²A/(1+cosA)(1-cosA)}×{(1-cosA)cosA}]/(1+sinA)

={cosA/(1+cosA)}/(1+sinA)

=cosA/(1+sinA)(1+cosA)

RHS

=sec²A(1-sinA)/(1+secA)

=(1/cos²A)(1-sinA)/(1+1/cosA)

={(1-sinA)/cos²A}/{(1+cosA)/cosA}

={(1-sinA)/(1-sin²A)}/{(1+cosA)/cosA}

={(1-sinA)/(1+sinA)(1-sinA)}/{(1+cosA)/cosA}

={1/(1+sinA)}/{(1+cosA)/cosA}

=cosA/(1+sinA)(1+cosA)

∴, LHS=RHS (Proved)

Hope this helped you!!!!

Answer 2

Answer:

REFER TO ATTACHMENT FOR ANSWER .

Legit Solved by KarnShubham ❤️