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Answer:

(1- sin^2 theta )sec ^2 theta

=( cos ^ 2 theta ) 1/ cos ^2 theta [[sin ^theta + cos^2 theta =1. and. sec ^2 theta = 1/ cos^2 theta]]

=1

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Answer:

Proof for : ( 1 - sin2 theta ) sec2 theta =1 is given as follows

To prove,

we know the trigonometric properties,

[tex](1-sin^2\theta)sec^2\theta \\

sin^2\theta + cos^2\theta \\

\Rightarrow 1-sin^2\theta [/tex]

Therefore, we have,

LHS:

[tex]= (1-sin^2\theta)sec^2\theta=(1−sin \\ = (cos^2\theta)sec^2[/tex]

we know the trigonometric ratios, given by,

[tex]cos\theta = \dfrac{1}{sec\theta} \\ \Rightarrow sec\theta=\dfrac{1}{cos\theta} \\ = (\dfrac{1}{sec^2\theta})[/tex]

:RHS

Hence the proof.