Question

cos^2theta +1/1+cot^2theta =1​

Answer 1

Step-by-step explanation:

To proof -

• cos²θ + 1/1+cot²θ = 1

As we know that :-

• cot²θ = cosec²θ - 1

Now,

→ cos²θ + 1/1+cosec²θ-1 = 1

→ cos²θ + 1/cosec²θ = 1

→ cos²θ + 1 ÷ 1/sin²θ = 1

→ cos²θ + sin²θ = 1

As we know that :-

• cos²θ + sin²θ = 1

→ 1 = 1

LHS = RHS

Hence,

Verified..

Some related formulas :-

• sin²θ + cos²θ = 1
• sec²θ - tan²θ = 1
• cosec²θ = 1 + cot²θ

Answer 2

$\large{\boxed{\underline{\underline{\bf{\red{Answer:-}}}}}}$

$\implies$ cos²(theta) + sin²(theta) = 1

$\implies$ 1 = 1

$\large\underline\mathrm{To \: proof}$

• Cos²(theta) + 1/1 + Cot²(theta) = 1
• Cot²(theta) = Cosec²(theta) - 1

$\large\underline\mathrm{Now,}$

$\implies$ Cos²(theta) + 1/1 - Cosec²(theta) = 1

$\implies$ Cos²(theta) + 1/Cosec²(theta) = 1

$\implies$ cos²(theta) ÷ sin²(theta) = 1

$\large\underline\mathrm{Then,}$

$\implies$ cos²(theta) + sin²(theta) = 1

$\implies$ 1 = 1

$\implies$ LHS = RHS

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