Question

Question 11
Simplify: $(1+ta{n}^2\theta )(1-sin\theta )(1+sin\theta )$

Answer 1

$(1+ta{n}^2\theta )(1-sin\theta )(1+sin\theta )=(1+ta{n}^2\theta )(1-si{n}^2\theta )$

$[\because (a-b\left)\right(a+b)=a^2-b^2]$

$=se{c}^2\theta .co{s}^2\theta$

$[\because 1+ta{n}^2\theta =se{c}^2\theta andco{s}^2\theta +si{n}^2\theta =1]$

$=\frac{1}{co{s}^2\theta }.co{s}^2\theta$ $[\because sec\theta =\frac{1}{cos\theta }]$

$=1(Ans.)$