Question

(1-sin∅)(sec∅+tan∅)=cos∅

Answer 1

Answer:

Hi your answer is as follows

Step-by-step explanation:

(1-sin)(sec + tan)

we know that sec = $\frac{1}{cos}$  and tan = $\frac{sin}{cos}$

substituting these values in the above equation we get,

(1-sin)($\frac{1}{cos}$+$\frac{sin}{cos}$)

(1-sin)($\frac{sin+1}{cos}$)

multiplying them we get,

$\frac{(1-sin)(1+sin)}{cos}$

we know that $a^{2} -b^{2} =(a-b)(a+b)$

so therefore in numerator we can substitute the formula ,

we get,

$\frac{1-sin^{2} }{cos}$

we also know that

$sin^{2}+ cos^{2} =1\\so,\\cos^{2} =1-sin^{2}$

substituting the above formula in numerator we get,

$\frac{cos^{2} }{cos}$

on simplification we get,

cos

therefore LHS = RHS

HENCE PROVED

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