TS EAMCET 5 May 2018 Shift 2 Solved Paper

Consider the function.
f(x)=sin‌5‌x.cos‌3‌x
It can be simplified as,
f(x)=

1

2

(2‌sin‌5‌x.cos‌3‌x)
=

1

2

(sin‌8‌x+sin‌2‌x)
Now, sin‌8‌x is periodic with period

2π

8

And, sin‌2‌x is periodic with period

2π

2

Therefore,
Period of f(x)=L.C.M{

π

4

,π}

L.C.M{π,π}

H.C.F{4,1}

=

π

1

π
So,
α=π
Hence,
cos‌α=cos‌π
=−1