Prove that 1+1/tan square A multiply by 1+1/cot squareA= 1/sin squareA-sin(power 4)A
Answers
Answered by
1
LHS= (1+cot^2A )(1+tan^2A)
(since,1/tan^2A=cot^2A)
=cosec^2A×sec^2A
(since,1+cot^2A=cosec^2A and
1+tan^2A=sec^2A)
=1/sin^2A×1/cos^2A
□NOW□
RHS= 1/sin^2A-sin^4A
=1/sin^2A (1-sin^2A)
(since,1-sin^2A=cos^2A)
=1/sin^2A×1/cos^2A
■■HENCE LHS=RHS PROVED■■
(since,1/tan^2A=cot^2A)
=cosec^2A×sec^2A
(since,1+cot^2A=cosec^2A and
1+tan^2A=sec^2A)
=1/sin^2A×1/cos^2A
□NOW□
RHS= 1/sin^2A-sin^4A
=1/sin^2A (1-sin^2A)
(since,1-sin^2A=cos^2A)
=1/sin^2A×1/cos^2A
■■HENCE LHS=RHS PROVED■■
Similar questions