Question

If Sin θ = 3/5 the value of (1 − Cos2 θ) is​

Answer 1

Answer:

9/25

Step-by-step explanation:

As per the information provided in the question, We have :

• Sin θ = 3/5

We are asked to find the value of (1 − Cos 2θ).

In order to find the value of (1 − Cos 2θ), We need to find the value of cos θ first. Then we can put the value of it the given expression.

As we know that, 3,4,5 is a Pythagorean triplet. Thus, The hypotenuse will be 5.

Here,

• Sin θ = 3/5

Sin = opp/hyp. Thus, 3 is opposite and 5 is the hypotenuse.

Cos θ will be,

• Cos = Base/hyp.

Base is 4 and hyp is 5. Hence, Cos θ is 4/5.

Putting the value of cos θ in (1 − Cos2 θ) :

⇒ $\rm 1 - \bigg({\dfrac{4}{5}}^{2}\bigg)$

Squaring the fraction.

⇒ $\rm 1 - \bigg(\dfrac{{4}^{2}}{{5}^{2}}\bigg)$

⇒ $\rm 1 - \dfrac{16}{25}$

Taking LCM,

⇒ $\rm \dfrac{1 \times 25}{25} - \dfrac{16}{25}$

⇒ $\rm \dfrac{1 \times 25 - 16}{25}$

On simplifying,

⇒ $\rm \dfrac{25 - 16}{25}$

⇒ $\rm \dfrac{9}{25}$

∴ The value of (1 − Cos 2θ) is 9/25.