Question

1/1+sin tita +1/1-sintita=2sec^2tita....maths

Answer 1

Step-by-step explanation:

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Answer 2

$\underline{\underline{\red{ANSWER}}}$

$\rm{\pink{Given\:Question\:Is}}$

$\implies{\rm{\frac{1}{1+Sin\theta}+\frac{1}{1-Sin\theta}=2Sec^2\theta}}$

$\underline{\underline{\rm{L.H.S}}}$

$\implies{\rm{\frac{1}{1+Sin\theta}+\frac{1}{1-Sin\theta}}}$

$\implies{\rm{\frac{1+Sin\theta+1-Sin\theta}{\left(1-Sin\theta\right)\left(1+Sin\theta\right)}}}$

$\implies{\rm{\frac{2}{1^2-Sin^2\theta}}}$

$\boxed{\pink{\rm{Becoz\:\left(a-b\right)\left(a+b\right)=a^2-b^2}}}$

$\implies{\rm{\frac{2}{1-Sin^2\theta}}}$

$\implies{\rm{\frac{2}{Cos^2\theta}}}$

$\boxed{\pink{\rm{Becoz\:\left(1-Sin^2\theta\right)=Cos^2\theta}}}$

$\implies{\rm{2Sec^2\theta}}$

$\boxed{\pink{\rm{Becoz\:\frac{1}{Cos^2\theta}=Sec^2\theta}}}$

$\implies{\rm{2Sec^2\theta}}$

$\therefore{\rm{\frac{1}{1+Sin\theta}+\frac{1}{1-Sin\theta}=2Sec^2\theta}}$

$\huge{\red{Hence\:,L.H.S=R.H.S}}$