If # tan theta + sec theta=x#,then prove that # sin theta =(x^2-1)/(x^2+1)# ?

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Answer 1 · 2017-08-14T15:15:47

If # tan theta + sec theta=x#,then prove that # sin theta =(x^2-1)/(x^2+1)#

Given
# tan theta + sec theta=x.....[1]#

# =>1/(sectheta+tantheta)=1/x#

# =>(sectheta-tantheta)/(sec^2theta-tan^2theta)=1/x#

# =>sectheta-tantheta=1/x....[2]#

Adding [1] and [2] we get

#2sectheta=x+1/x....[3]#

Subtracting [2] from [1] we get

#2tantheta=x-1/x....[4]#

Dividing [4] by [3] we get

#tantheta/sectheta=(x-1/x)/(x+1/x)#

#=>sintheta=(x^2-1)/(x^2+1)#