Simplify the expressioncos theta1 sin theta tan thetaSolut

Simplify the expression.cos theta/1 + sin theta + tan theta

Solution

I am taking x in place of theta

Cosx/1+sinx +Tanx=cosx/1+sinx +sinx/cosx

=Cosx×cosx +sinx×(1+sinx)/(1+sinx)cosx

=Cos^2x+sin^2x+sinx/(1+sinx)cosx

Since sin^2x+cos^2x=1,so it becomes,1+sinx/(1+sinx)cosx

1/cosx= secx