यदि `sec theta + tan theta =x` तो `sec theta, tan theta` `sin theta` के मान ज्ञात करो।

Explanation

दिया है: `sec theta+ tan theta =x.`
`therefore sec ^(2) theta -tan ^(2) theta =1`
`implies (sec theta +tan theta )(sec theta - tan theta )=1`
`implies x(sec theta - tan theta)=1" "[because sec theta +tan theta =x]`
`implies sec theta -tan theta =1/x`
अतः
`sec theta + tan theta =x` अथवा ` sec theta -tan theta =(1)/(x)`
दोनों समीकरणों को जोड़ने तथा घटाने पर
`2 sec theta =x+(1)/(x) ` तथा `2 tan theta=x -1/x`
`impliessec theta =1/2 (x+(1)/(x))` तथा `tan theta=1/2 (x-(1)/(x))`
`therefore sin theta =(tan theta)/(sec theta)impliessin theta =(1/2(x-(1)/(x)))/(1/2(x+(1)/(x)))=(x^(2)-1)/(x^(1)+1)`