Math, asked by aneri2435, 1 year ago

If x is equal to 1 minus sin 2x + cos2x upon 2 cos 2x then find the value of f of 16 degree into a 29 degree

Answers

Answered by pinquancaro
0

Answer:

f(16)\times f(29)=\frac{1}{2}

Step-by-step explanation:

Given : Expression f(x)=\frac{1-\sin 2x+\cos 2x}{2\cos 2x}

To find : The value of f(16)\times f(29)

Solution :

First we solve the expression,

f(x)=\frac{1-\sin 2x+\cos 2x}{2\cos 2x}

f(x)=\frac{1-\sin 2x}{2\cos 2x}+\frac{\cos 2x}{2\cos 2x}

f(x)=\frac{\cos^2x+\sin^2x-2\sin x\cos x}{2(\cos^2x-\sin^2x)}+\frac{1}{2}

f(x)=\frac{(\cos x-\sin x)^2}{2(\cos x-\sin x)(\cos x+\sin x)}+\frac{1}{2}

f(x)=\frac{\cos x-\sin x}{2(\cos x+\sin x)}+\frac{1}{2}

f(x)=\frac{1}{2}(\frac{\cos x-\sin x}{\cos x+\sin x}+1)

f(x)=\frac{1}{2}(\frac{1-\tan x}{1+\tan x}+1)

f(x)=\frac{1}{2}(\tan(45-x)+1)

Now, put x=16 and x=19

f(16)\times f(29)=\frac{1}{2}(\tan(45-16)+1)\times \frac{1}{2}(\tan(45-29)+1)

f(16)\times f(29)=\frac{1}{4}(\tan(29)+1)\times(\tan(16)+1)

f(16)\times f(29)=\frac{1}{4}(\tan(29)(\tan(16)+\tan(29)+\tan(16)+1)

We know, \frac{\tan(29)\tan(16)}{1-\tan(29)\tan(16)}=1

So, \tan(29)(\tan(16)+\tan(29)+\tan(16)=1

f(16)\times f(29)=\frac{1}{4}(1+1)

f(16)\times f(29)=\frac{1}{4}(2)

f(16)\times f(29)=\frac{1}{2}

Therefore, The value is f(16)\times f(29)=\frac{1}{2}

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