Question

Find the value of cos²x if sin x = 3/5​

Answer 1

$cos^2x=\frac{16}{25}$

Step-by-step explanation:

$\Large \bf \underline{Given:}$

$sin x = \frac{3}{5}$

$\Large \bf \underline{To\:Find:}$

Value of cos²x

$\Large \bf \underline{Solution:}$

We know that,

$\bf\underline{ \boxed{sin^{2}x +cos^{2}x=1}}$

$\implies \bf\underline{cos^{2}x=1-sin^{2}x}$

$sin\:x=\frac{3}{5}$

Now, putting values in the above formula;

$cos^{2}x=1-(\frac{3}{5})^2\\\\\\cos^2x= 1-\frac{9}{25}\\\\\\\implies \bf \underline{\boxed{cos^2x=\frac{16}{25}}}$

_______________________________

$\Large\bf Know\:more:-$

• $\bf\underline{\boxed{sec^2x-tan^2x=1}}$

• $\bf\underline{\boxed{cosec^2x-cot^2x=1}}$

Answer 2

Given

sinx = 3/5

We know a formula

cos2x = ( 1 - 2sin²x)

Putting the value of sinx on value of cos2x = ( 1 - 2sin²x)

hence,

we get

cos2x = ( 1 - 2sin²x )

=> [1 - 2 × ( 3/5 )² ]

=> [ 1 - 2 × 9 /25 )

=> [ 25 - 18 /25 ]

=> 7/25 Answer