Question

If 3sin theta - 4cos theta = 0. then , find the values of tan theta , sec theta & cosec theta.

Answer 1

 solution

3sinФ - 4cosФ=0

3sinФ=4cosФ

⇒ sinФ/cosФ=4/3

⇒ tanФ=4/3

⇒ tanФ=4/3

then the value of

tanФ=4/3

for 1 + tan²Ф=sec²Ф

⇒ 1 + 4/3=sec²Ф

⇒√ (3+4)/3=secФ

⇒ secФ=√7/3

for cosec²Ф=cot²Ф+1

⇒cosec²Ф=3/4+1

cosecФ=√7/4

Answer 2

$tan\theta=\dfrac{4}{3},sec\theta=\dfrac{5}{3},cosec\theta=\dfrac{5}{4}$

Step-by-step explanation:

Here, $3\:sin\theta-4\:cos\theta=0$

$\Rightarrow 3\:sin\theta=4\:cos\theta$

$\Rightarrow tan\theta=\dfrac{4}{3}$

Then, vertical is 4 and base is 3.

So, hypotenuse is $\sqrt{4^{2}+3^{2}}$

$=\sqrt{16+9}=\sqrt{5}=5$

Now, $sec\theta$

$=\dfrac{hypotenuse}{base}$

$=\dfrac{5}{3}$

and $cosec\theta$

$=\dfrac{hypotenuse}{vertical}$

$=\dfrac{5}{4}$

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