Prove that :-
(coses A - sin A) ( sec A - cos A) = 1/tanA+cotA
Answers
Answered by
1
Answer:
taking L. H. S =
(cosecA - sinA)×(secA - cosA)
= (1/sinA - sinA)×(1/cosA - cosA)
= (1-sin²A)/sinA × (1-cos²A)/cosA
= cos²A/sinA × sin²A/cosA
= cos²Asin²A/cosAsinA
= cosAsinA
Now, R. H. S =
1/(tanA + cotA)
= 1/(sinA/cosA + cosA/sinA)
= 1/[(sin²A + cos²A)/cosAsinA]
= 1/[(1/cosAsinA)]
= cosAsinA
Since L. H. S. = R. H. S.
Therefore the given equation is proof.
Similar questions