cot A - 1/ 2- sec square A = cot A / 2+ tan A
prove the question
Attachments:
Answers
Answered by
1
Answer:
Hey Friend,
cotA - 1 / 2 - sec^2A = cotA / 1 + tanA
LHS
= cotA - 1 / 2 - sec^2A
= (cosA/sinA - 1) / 1 + 1 - sec^2A
= [(cosA - sinA) / sinA] / 1 - tan^2A
= [(cosA - sinA) / sinA] / [1 - sin^2A / cos^2A]
= [(cosA - sinA) / sinA] / [(cos^2A - sin^2A) / cos^2A]
= (cosA - sinA) / sinA X cos^2A / (cosA + sinA) (cosA - sinA)
= cos^2A / sinA (cosA + sinA)
RHS
= cotA / 1 - tanA
= (cosA / sinA) / (1 - sinA/cosA)
= (cosA / sinA) / [(cosA - sinA) / cosA]
= cosA / sinA X cosA / (cosA - sinA)
= cos^2A / sinA (cosA + sinA)
LHS = RHS
Hence proved.
Hope it helps!
Similar questions