24 a. If tan θ + 1/tan θ = 2, find the value of tan^2 θ + 1/tan^2 θ

Question

Q) If tan θ + 1 / tan θ = 2, find the value of tan^2 θ + 1/ tan^2 θ.
(Q 24 A - 30/2/1 - CBSE 2026 Question Paper)

Sapling Academy · Accepted Answer

Step 1: Given that, $	an 	heta + \frac{1}{	an 	heta} = 2$
By squaring on both sides we get:
$(	an 	heta + \frac{1}{	an 	heta})^2 = (2)^2$
∴ $(	an 	heta + \frac{1}{	an 	heta})^2 = 4$
Step 2: ∵ (a + b) 2 = a 2 + b 2 + 2 a b
∴ Our expression becomes:
$(	an 	heta + \frac{1}{	an 	heta})^2 = 4$
∴ $(	an 	heta)^2 + (\frac{1}{	an 	heta})^2 + 2 (	an 	heta) 	imes (\frac{1}{	an 	heta}) = 4$
∴ $(	an 	heta)^2 + (\frac{1}{	an 	heta})^2 + 2 \cancel{(	an 	heta)} 	imes (\frac{1}{\cancel{	an 	heta}}) = 4$
∴ $	an^2 	heta + \frac{1}{	an^2 	heta} + 2 = 4$
∴ $	an^2 	heta + \frac{1}{	an^2 	heta} = 4 - 2 = 2$
Therefore, the value of $	an^2 	heta + \frac{1}{	an^2 	heta}$ is 2.
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