Question

If cos theta + cos square theta equal to 1 the value of sin theta + sin power 4 theta is?
Please tell answer with explaination

Answer 1

Trigonometric Identities

We've been provided with an equation $\cos(\theta) + \cos^2(\theta) = 1$ and we've been asked to find out the value of $\sin^2(\theta) + \sin^4(\theta)$.

Let's head to the Question now:

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

Now, on squaring both sides, we get;

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

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

$\implies \sin^2(\theta) + \sin^4(\theta) \\ \\ \implies \cos(\theta) + \cos^2(\theta) \\ \\ \implies \boxed{1}$

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

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MORE TO KNOW

1. Relationship between sides and T-Ratios.

• sin(θ) = Height/Hypotenuse
• cos(θ) = Base/Hypotenuse
• tan(θ) = Height/Base
• cot(θ) = Base/Height
• sec(θ) = Hypotenuse/Base
• cosec(θ) = Hypotenuse/Height

2. Square formulae.

• sin²(θ) + cos²(θ) = 1
• 1 + tan²(θ) = sec²(θ)
• 1 + cot²(θ) = cosec²(θ)

3. Reciprocal Relationship.

• sin(θ) = 1/cosec(θ)
• cos(θ) = 1/sec(θ)
• tan(θ) = 1/cot(θ)
• cot(θ) = 1/tan(θ)
• sin(θ)/cos(θ) = 1/cot(θ)
• cos(θ)/sin(θ) = 1/tan(θ)
• sin2(θ) = 2sin(θ)cos(θ)
• cos2(θ) = cos²(θ) - sin²(θ)