Question

25.5.21
Prove the following indambities. -
1. tam ²0 + cot? 0 +2 = See ²0 cosic²a​

Answer 1

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