Practicing Success
If $\frac{1+sinθ-cosθ}{1+sinθ+cosθ}+\frac{1+sinθ+cosθ}{1+sinθ-cosθ}=4$, then which of the following values will be suitable for θ ? |
90° 60° 45° 30° |
30° |
$\frac{1+sinθ-cosθ}{1+sinθ+cosθ}+\frac{1+sinθ+cosθ}{1+sinθ-cosθ}=4$ \(\frac{( 1+sinθ-cosθ)² + ( 1+sinθ+cosθ)² }{(1+sinθ)² - cos²θ}\) = 4 \(\frac{ 1 +sin²θ +cos²θ+2 sinθ-2cosθ -2sinθcosθ + 1 +sin²θ +cos²θ+2 sinθ-2cosθ -2sinθcosθ}{ 1+sin²θ +2 sinθ - cos²θ}\) = 4 \(\frac{( 4+4sinθ }{ 1+ sin²θ + 2sinθ - (1 - sin²θ)}\) = 4 \(\frac{( 4(1+sinθ) }{ 2sinθ(1+sinθ)}\) = 4 \(\frac{2 }{ sinθ}\) = 4 sinθ = \(\frac{1 }{ 2}\) { we know, sin30º = \(\frac{1 }{ 2}\) } So, θ = 30º |