Question

if sec ^2theeta (1+sintheta)(1-sintheta )=k then find the value of k

Answer 1

hope this helps you☺️

Answer 2

$Given, \: sec^{2}\text{A \: ( 1 + sinA ) ( 1 - sinA ) = k}$



Solving Left Hand Side ,

$sec^{2}A [ ( 1 - sin A) ( 1 - sin A) ]$



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We know, ( a - b ) ( a + b )
Assume, a = 1
b = sinA
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$sec^{2} A ( 1^{2} - sin^{2} A ) \\ \\ \\ sec^{2}A ( cos^{2}A ) \:\:\:\:\:\:\:\:\:\:\: | \bold{ 1 - sin^{2}A = cos^{2} A }\\ \\ \\ \\ sec^{2} A \times cos^{2}A \\ \\ \\ sec^{2}A \times \frac{1}{sec^{2}A} \:\:\:\:\:\:\:\:\: \bold{ | cos^{2} = \frac{1}{ {sec}^{2}A } } \\ \\ \\ \: We \: \: know \\ \\ \\ \\ LHS = RHS \\ 1 = k \\ Comparing \: value, \: we \: get \: that \: the \: value \: of \: k \: i s \: 1 \:$