Question

prove that (1+cotA=tanA)(sinA+cosA)=secA/cosec^2A - cosecA/sec^2A

Answer 1

Heya!!! ✌️✌️

Here is your answer dear....
(1+cotA+tanA)(sinA-cosA)= (1+cosA/sinA+sinA/cosA)(sinA-cosA)
= (sinAcosA+sin^2A+cos^2A / sinAcosA)(sinA-cosA)
= (sinAcosA+1 /sinAcosA )(sinA-cosA)
=cosecAsecA(sinAcosA+1)(sinA-cosA)
=cosecAsecA(sin^2acosA+sinA-sinAcos^2A-cosA)
=cosecAsecA(cosA{sin^2A-1)-sinA{cos^2A-1})
=cosecAsecA(cos^3A-sin^3A)
=cosecAsecA(1/sec^3A-1/cosec^3A)
multipty cosecAsecA inside we get
=secA/cosec^2A-cosecA/sec^2a

I HOPE THIS WILL HELP YOU OUT....

HAVE A GREAT DAY DEAR....

#Bhavana ☺️