Question

Sectheta +tantheta =1/5 then sin theta

Answer 1

Step-by-step explanation:

it will help you dear......

Answer 2

Answer:

$\frac{12}{13}$ is the required value of $sin\theta$

Step-by-step explanation:

Explanation:

Given ,  $sec\theta + tan\theta = \frac{1}{5}$

Let $sec\theta + tan\theta = \frac{1}{5}$ ......(i)

 As we know that  $1 + tan^2\theta = sec^2 \theta$

Step 1:

Therefore , we can written $1 + tan^2\theta = sec^2 \theta$ as $sec^2\theta - tan ^2\theta = 1$.

Now , from the formula  of $a^2 - b^2 = (a+ b)(a-b)$ we get ,

$(sec\theta + tan\theta )(sec\theta - tan\theta )$ = 1

But  from the question we have , $sec\theta + tan\theta = \frac{1}{5}$ .

⇒ $\frac{1}{5}$ $(sec\theta - tan\theta )$ = 1 ⇒ $sec\theta - tan\theta = 5$ .....(ii)

Step 2:

Adding (i) and (ii) we get ,

($sec\theta + tan\theta$ ) + ($sec\theta - tan\theta$) = $\frac{1}{5} + 5$

⇒2$sec\theta = \frac{26}{5}$  ⇒     $sec\theta = \frac{13}{5}$

Therefore , $sec \theta = \frac{h}{b}$  where h is hypotenuse  and b is base  of a triangle .

So ,  we have h = 13 and b = 5  .

By using  Pythagoras theorem  

Perpendicular (p)  =  $\sqrt{h^2- b^b}$

⇒p = $\sqrt{13^2- 5^2}$   ⇒ p = $\sqrt{169 - 25 }$ = $\sqrt{144}$ = 12

And  $sin\theta = \frac{p}{h}$ ⇒ $sin\theta$ =  $\frac{12}{13}$               [p = 12 and h = 13 ]

Final answer:

Hence , the value of $sin\theta \ is \frac{12}{13}$ .

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