Question

निम्नलिखित वाक्यों में सही स्थान पर उचित विराम चिन्ह लगाइए १. वाह आपने तो कमाल कर दिया २. क्या तुम विद्यालय गए थे - तितलिरिवत वाक्यों का वचन-परिवर्तन करके वाक्य फिर से लि
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Answer 1

Explanation:

Trigonometric Identities

We've been provided with an equation \cos(\theta) + \cos^2(\theta) = 1cos(θ)+cos

2

(θ)=1 and we've been asked to find out the value of \sin^2(\theta) + \sin^4(\theta)sin

2

(θ)+sin

4

(θ) .

Let's head to the Question now:

\begin{gathered} \implies \cos(\theta) + \cos^2(\theta) =1 \\ \\ \implies \cos(\theta) =1- \cos^2(\theta) \\\\ \implies \cos(\theta) = \sin^2(\theta) \qquad \bf{....(1)}\end{gathered}

⟹cos(θ)+cos

2

(θ)=1

⟹cos(θ)=1−cos

2

(θ)

⟹cos(θ)=sin

2

(θ)....(1)

Now, on squaring both sides, we get;

\begin{gathered}\implies (\cos(\theta))^2 = (\sin^2(\theta))^2\\\\ \implies \cos^2(\theta) = \sin^4(\theta) \bf{\qquad....(2)}\end{gathered}

⟹(cos(θ))

2

=(sin

2

(θ))

2

⟹cos

2

(θ)=sin

4

(θ)....(2)

Now, by substituting the values of equation (1) and equation (2) in \sin^2(\theta) + \sin^4(\theta)sin

2

(θ)+sin

4

(θ) , we get:

\begin{gathered}\implies \sin^2(\theta) + \sin^4(\theta) \\ \\ \implies \cos(\theta) + \cos^2(\theta) \\ \\ \implies \boxed{1}\end{gathered}

⟹sin

2

(θ)+sin

4

(θ)

⟹cos(θ)+cos

2

(θ)

⟹

1

Hence, the value of sin²(θ) + sin⁴(θ) is 1.

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