Question

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

Answer 1

Solution :

Now,

L.H.S. = ( 1 - tan²θ ) / ( 1 + tan²θ )

= { 1 - ( sin²θ / cos²θ ) } / { 1 + ( sin²θ / cos²θ ) }

= { ( cos²θ - sin²θ ) / cos²θ } / { ( cos²θ + sin²θ ) / cos²θ }

= cos²θ - sin²θ, since cos²θ + sin²θ = 1

= R.H.S.

Hence, proved.

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