Prove that :Cos theta /1-sin theta = sec theta +tan theta ?

2 Answers
Feb 23, 2018

The LHS of the proving statement is given as #Cos theta /(1-sin theta) #

Multiply and divide by #(1+sin theta)#

#=(Cos theta(1+sin theta)) /((1-sin theta)(1+sin theta)) #

#=(Cos theta + costhetasintheta) /(1-sin^2 theta) #

By the identity, #sin^2theta + cos^2theta=1#,

#=(Cos theta + costhetasintheta) /(cos^2 theta) #

#=cancelCos theta/cancel((costheta)^2)^1 + (cancelcosthetasintheta)/cancel((costheta)^2)^1 #

#=1/costheta + sintheta/costheta#

#=sectheta + tantheta#

#"Hence proved!"#

Feb 23, 2018

#"see explanation"#

Explanation:

#"consider the left side"#

#costheta/(1-sintheta)#

#"multiply numerator/denominator by "(1+sintheta)#

#=(costheta(1+sintheta))/((1-sintheta)(1+sintheta))#

#=(costheta+costhetasintheta)/(1-sin^2theta)#

#=(costheta+costhetasintheta)/cos^2theta#

#=1/costheta+sintheta/costheta#

#=sectheta+tantheta=" right side "rArr" proved"#