1.

I Know The Answer (c). Plz explain It..

Answer»

Step-by-step explanation:

tan θ + sin θ = x

tan θ - sin θ = y

from the above two EQUATIONS, we get

=> 2 sin θ = x - y

      sin θ = (x - y)/2                    [ we will substitute this value later]

also, in the above two equations TAKING tan θ as COMMON we get,

tan θ (1 + cos θ) = x

tan θ (1 - cos θ) = y

dividing the above equations,

=> ​(1 + cos θ)/(1 - cos θ) = x/y

y + y cos θ = x - x cos θ

x - y = y cos θ + x cos θ

cos θ (x + y) = x - y

cos θ =  \frac{x-y}{x+y}

squaring on both SIDES,

cos² θ = (\frac{x-y}{x+y})^{2}                               [ sin²θ + cos²θ = 1]

1 - sin²θ = (\frac{x-y}{x+y})^{2}

1-(\frac{x-y}{2})^{2} = \frac{(x-y)^{2}}{(x+y)^{2}}\\\\ 1-\frac{(x-y)^{2}}{4} =\frac{(x-y)^{2}}{(x+y)^{2}} \\\\ (x+y)^{2} - \frac{(x-y)^{2} (x+y)^{2}}{4} =(x-y)^{2} \\\\ (x+y)^{2} - (x-y)^{2}=\frac{(x^{2}-y^{2})^{2}}{4} \\\\4xy = \frac{(x^{2}-y^{2})^{2}}{4} \\\\x^{2}-y^{2} = \sqrt{16xy} \\\\x^{2}-y^{2} = 4\sqrt{xy} \\\\\\\ HOPE \ YOU \ GOT \ IT! \\\\\ THANKS


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