Question

if sin theta = cos theta, then the value of tan square theta + cot square theta is​

Answer 1

Answer:

2

Explanation:

see picture for ans..........

Answer 2

tan²θ + cot²θ = 2

Given :

sinθ = cosθ

To find :

The value of tan²θ + cot²θ

Solution :

Step 1 of 2 :

Find the value of tanθ and cotθ

Here it is given that

$\displaystyle \sf sin\theta = cos\theta$

$\displaystyle \sf{ \implies } \frac{sin\theta }{ cos\theta} = 1$

$\displaystyle \sf{ \implies }tan\theta = 1$

Again

$\displaystyle \sf cot \theta= \frac{1}{tan\theta} = \frac{1}{1} = 1$

Step 2 of 2 :

Find the value of tan²θ + cot²θ

$\displaystyle \sf {tan}^{2} \theta + {cot}^{2} \theta$

$\displaystyle \sf = {1}^{2} + {1}^{2}$

$\displaystyle \sf = 1 + 1$

$\displaystyle \sf = 2$

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