Question

If sina=1/3 then find the value of 2cot^2a+2

Answer 1

if sinA=1/3
Then 2cot²A+2
=2(cot²A+1)
=2cosec²A. [` . ` cot²A+1=cosec²A] =2(1/sinA)² [' . ' cosecA=1/sinA]
=2×3²/1
= 18 ..Ans

Answer 2

Answer:

18

Step-by-step explanation:

Given,

$sin a = \frac{1}{3}$ -----(1)

$\sqrt{1-cos^2a}=\frac{1}{3}$     ( sin² a + cos² a = 1 ⇒ sin² a = 1 -  cos² a ⇒ sin a = √(1-cos²a) )

$1-cos^2a=\frac{1}{9}$

$-cos^2a=\frac{1}{9}-1$

$-cos^2a=-\frac{8}{9}$

$cos^2a=\frac{8}{9}$ -------(2)

Now,

$cot a = \frac{cos a}{sin a}$

$\implies cot^2a = \frac{cos^2a}{sin^2a}=\frac{\frac{8}{9}}{\frac{1}{9}}=8$---(3)

Thus,

$2 cot^2a+2=2\times 8+2 = 16+2=18$ ( From equation (3) )