TS EAMCET 5 May 2018 Shift 1 Solved Paper

The expression is given as,
sin‌

π

2n

+cos‌

π

2n

=

√n

2

…… (1)
Square both the sides,
(sin‌

π

2n

+cos‌

π

2n

)2=

n

4

Further simplify then,
sin‌

π

n

=

n−4

4

since, sin‌

π

n

>0,n>2 then

n−4

4

>0
n>4 …… (2)
The equation is,
sin(

π

2n

)+cos‌

π

2n

=√2‌sin(

π

4

+

π

2n

)
From equation ( 1 ),
√2‌sin(

π

4

+

π

2n

)=

√n

2

sin(

π

4

+

π

2n

)=

√n

2√2

since, sin(

π

4

+

π

2n

)<1,∀n>2 then

√n

2

<1
n<8 …… (3)
From equation (2) and equation (3),
$4 So, n=5,6,7
Thus, the number of integral value of n is 3 .