Show how to prove that the first expression is identical to the second expression.?

Question

First expression: #(1-tan^2 theta)/(1+sin^2 theta)#

Second expression: #(2/cos^2 theta) - 1#

#(1-tan^2 theta)/(1+sin^2 theta)# ≡ #(2/cos^2 theta) - 1#

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Answer 1 · 2018-04-01T16:09:07

#color(red)((1-tan^2(theta))/(1+sin^2(theta))!=(2/cos^2(theta))-1#

#(1-tan^2(theta))/(1+sin^2(theta))=(2/cos^2(theta))-1#

Let # \ \ \ \ theta=pi/3#

#(1-tan^2(pi/3))/(1+sin^2(pi/3))=(2/cos^2(pi/3))-1#

#(-2)/(7/4)=2/(1/4)-1#

#-8/7=7color(white)(88)# This is false

Therefore:

#color(red)((1-tan^2(theta))/(1+sin^2(theta))!=(2/cos^2(theta))-1#