Question

prove that(1- sin 2x) /(1+sin 2x) =
tan²(π/4 -x)
$\frac{(1 - \sin(2x) )}{(1 - \sin(2x) )} = \ {{tan(( \frac{\pi}{4} ) - x}})^{2}$
class 11​

Answer 1

$\underline {\textbf{\large {Step by step explanation }}}$

$\underline {\textbf{\large{To prove:}}}$

$\frac{(1 - \sin(2x) )}{(1 + \sin(2x) )} = \ {{tan^2(( \frac{\pi}{4} ) - x}})$

$\underline {\textbf{\large{proof:}}}$

[refer the attachment for the proof ]

${\textbf{\large{LHS = RHS}}}$

hence proved.

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$\underline {\textbf{\large{formulae used:}}}$

1)) sin²Φ + cos²Φ = 1

2)) ( a + b) ² = a² + b² + 2ab

3)) ( a - b ) ² = a² + b² - 2ab

4)) $tan (A - B) = \frac{tanA - tanB}{1 + tanA. tanB }$