25.5.21
Prove the following indambities. -
1. tam ²0 + cot? 0 +2 = See ²0 cosic²a
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Answer:
Let o=A,
tan2A+cot2A+2= sec2A.cosec2A
by LHS
tan2A+2+cot2A
=tan2A+2tanA.cotA+cot2A {tanA.cotA=1}
=(tanA+cotA)^2. {a2+2ab+b2=(a+b)^2}
=(sinA/cosA+cosA/sinA/cosA)^2
=(sin^2A+cos^A/sinA.cosA)^2
=(1/sinA.cosA)^2
=1/sin^2A.cos^2A
= 1/sin^2A×1/cos^A
=cosec^2A.sec^2A
sec^2A.cosec^2A=RHS hence proved
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