Question

prove that, sinθ(1+tanθ)+cosθ(1+cotθ)=secθ+cosecθ​

Answer 1

Step-by-step explanation:

SinΘ(1+tanΘ)+cosΘ(1+cotΘ)=secΘ+cosecΘ

By LHS:

=SinΘ(1+tanΘ)+cosΘ(1+cotΘ)

=SinΘ(1+sinΘ/cosΘ)+cosΘ(1+cosΘ/sinΘ)

=SinΘ.cosΘ+sin²Θ/cosΘ+cosΘ.sinΘ+cos²Θ/sinΘ

=sin²Θ.cosΘ+sin³Θ+cos²Θ.sinΘ+cos³Θ/sinΘ.cosΘ

=cos²Θ.sinΘ+sin³Θ+sin²Θ.cosΘ+cos³Θ/sinΘ.cosΘ

=SinΘ(cos²Θ+sin²Θ)+cosΘ(sin²Θ.cos²Θ)/sinΘ.cosΘ

=SinΘ(1)+cosΘ(1)/sinΘ.cosΘ

=SinΘ/sinΘ.cosΘ+cosΘ/sinΘ.cosΘ

=1/cosΘ+1/sinΘ

=secΘ+cosecΘ

.•.RHS=LHS

hope it helps!!!

Answer 2

hope that helps you :-)