1.

What is the simplified value of \({\left[ {\frac{{co{s^2}\theta }}{{1\; + \;\sin \theta }} - \frac{{si{n^2}\theta }}{{1\; + \;\cos \theta }}} \right]^2}\)?1). sinθ2). 1 – sin2θ3). 1 + sin2θ4). 1 – sinθ

Answer»

Since all the options have sinθ in them, we can CONCLUDE by seeing that they all give DIFFERENT VALUES.

Putting θ = 45°

We get the values of options as :

(1) 1/√2

(2) 0

(3) 2

(4) (√2 – 1)/√2

Value asked in question = [(1/2)/(1 + (1/√2)) – (1/2)/(1 + (1/√2))]2 = 0

∴ the answer is (2)



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