Question

Prof that √1+sina/1-sina = seca + tana ×points is 30tha
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Answer 1

ANSWER.......................

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Answer 2

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$\tt\:LHS=\sqrt{\dfrac{1+sinA}{1-sinA}}$

Rationalize the denominator,

$\tt\longrightarrow\:\sqrt{\dfrac{(1+sinA)}{(1-sinA)}\times\:\dfrac{(1+sinA)}{(1+sinA)}}$

$\tt\longrightarrow\:\sqrt{\dfrac{(1+sinA)^2}{{(1)}^{2}-{(sinA)}^{2}}}$

$\tt\longrightarrow\:\sqrt{\dfrac{(1+sinA)^2}{1-si{n}^{2}A}}$

$\tt\longrightarrow\:\sqrt{\dfrac{(1+sinA)^2}{co{s}^{2}A}}$

$\tt\longrightarrow\:\dfrac{1+sinA}{cosA}$

$\tt\longrightarrow\:\dfrac{1}{cosA}+\dfrac{sinA}{cosA}$

$\tt\longrightarrow\:secA+tanA$

$\tt\:LHS=RHS$

$\rm\:Hence,proved$

$\blue{\bigstar}\:\:{\underline{\boxed{\bf\red{More\:Information}}}}$

✪ Trigonometric Identity :- An equation involving trigonometric ratios of an angle is called a trigonometric identity if it is true for all values of the angle.

• sin²θ + cos²θ = 1

• 1 + tan²θ = sec²θ

• 1 + cot²θ = cosec²θ

• tanθ = sinθ/cosθ

• cotθ = cosθ /sinθ

• tanθ × cotθ = 1