Question

sin theta (1+ tan theta)+ cos theta(1+ cot theta) = ( sec theta + cosec theta)​

Answer 1

Answer:

Prove that: sinθ(1+tanθ)+cosθ(1+cotθ)=secθ+cosecθ

Step-by-step explanation:

sinθ(1+tanθ)+cosθ(1+cotθ)

=sinθ+  

cosθ

sin  

2

θ

​

+cosθ+  

sinθ

cos  

2

θ

​

 

=sinθ+  

sinθ

cos  

2

θ

​

+  

cosθ

sin  

2

θ

​

+cosθ

A=  

sinθ

sin  

2

θ+cos  

2

θ

​

+  

cosθ

sin  

2

θ+cos  

2

θ

​

 

As,sin  

2

θ+cos  

2

θ=1

A=  

sinθ

1

​

+  

cosθ

1

​

 

= cosecθ+secθ

​