cos[π^2]θ sin[e]θ = [π^2]=[3.14^2]=[9.85]=9 [e]=[2.7]=2 ⇒cos[π^2]θ sin[e]θ =cos 9θ sin 2θ ⇒cos 9θ +cos(π2+2θ) ⇒ 2cos[9θ +π2+2θ2 ...

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Greatest Integer Function

cos [π2]θ-sin...

Question

$cos [π^{2}] θ - sin [e] θ =$ ?

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Solution

$cos [π^{2}] θ - sin [e] θ =$

$[π^{2}] = [{3.14}^{2}] = [9.85] = 9$

$[e] = [2.7] = 2$

$\Rightarrow cos [π^{2}] θ - sin [e] θ = cos 9 θ - sin 2 θ$

$\Rightarrow cos 9 θ + cos (\frac{π}{2} + 2 θ)$

$\Rightarrow 2 cos ⎡ ⎢ ⎢ ⎣ \frac{9 θ + \frac{π}{2} + 2 θ}{2} ⎤ ⎥ ⎥ ⎦ cos ⎡ ⎢ ⎢ ⎣ \frac{9 θ + \frac{π}{2} - 2 θ}{2} ⎤ ⎥ ⎥ ⎦$

$\Rightarrow 2 cos [\frac{π}{4} + \frac{11 θ}{2}] cos [\frac{π}{4} - \frac{7 θ}{2}]$

$∴ cos [π^{2}] θ - sin [e] θ = 2 cos [\frac{π}{4} + \frac{11 θ}{2}] cos [\frac{π}{4} - \frac{7 θ}{2}]$ .

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