Question

if sin theta =½,then,1+2sin²theta =​

Answer 1

Answer:

Correct option is

C

2nπ+

6

7π

The sum of two squared terms being 0 implies both the terms are individually 0!

Thus, sinθ=

2

−1

, implying θ=2nπ+sin

−1

(

2

−1

)=(2n+1)π+

6

π

Also, the other term says tanθ=

3

1

, implying θ=kπ+

6

π

Thus, the general solution combining the two will be (

6

π

+ odd multiples of π), or 2nπ+

6

7π

Answer 2

Given,

$\[\sin \theta = \frac{1}{2}\]$

Solution,

$\[ = 1 + 2{\sin ^2}\theta \]$

$\[ = 1 + 2 \times {\left( {\frac{1}{2}} \right)^2}\]$

$\[ = 1 + 2 \times \frac{1}{4}\]$

Simplify it,

$\[ = 1 + \frac{1}{2}\]$

$\[ = \frac{3}{2}\]$

Hence the solution is $\[\frac{3}{2}\]$.