If A is not an integral multiple of , 2
then prove that
(i) tan A + cot A = 2 cosec 2A (ii) cot A - tan A= 2 cot 2A
Answers
Given : tan A + cot A = 2 cosec2A
cotA - tan A = 2 cot2A
To Find : Prove
Solution:
tan A + cot A = 2 cosec2A
LHS
= tan A + cot A
= SinA/cosA + cosA/sinA
= (sin²A + cos²A)/cosAsinA
= 1/cosA.sinA
=2/2sinA.cosA
= 2/sin2A
= 2cosec2A
= RHS
QED
cotA - tan A = 2 cot2A
LHS
= cotA - tanA
= cosA/sinA - sinA/cosA
= (cos²A - sin²A)/sinA.cosA
= cos2A/sinA.cosA
= 2cos2A/2sinA.cosA
= 2cos2A/sin2A
= 2cot2A
= RHS
QED
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