Question

If 6 cot theta + 2 cosecA theta = cot theta + 5 cosec theta , find the value of cos theta.

Answer 1

hey 6 cotA + 2 cosec A = cotA + 5cosec A

so, 6*cosA/sinA + 2/sinA = cosA/sinA + 5/sinA

                          = 5 cosA/sinA -3/sinA = 0
                       so, 5cos A-3/sinA =0
                      so , 5 cos A - 3 = 0
                                 cos A = 3/5        

hope this helps plz mark as brainliest

Answer 2

Answer:

The value of cos $\theta$ = $\frac{3}{5}$

Step-by-step explanation:

Given,

6 cot $\theta$+ 2 cosec $\theta$ = cot $\theta$ + 5 cosec $\theta$

To find,

The value of cos $\theta$

Recall the formula

cot $\theta$ = $\frac{cos\theta}{sin\theta}$

cosec  $\theta$ = $\frac{1}{sin\theta}$

Solution:

Given equation is 6 cot $\theta$+ 2 cosec $\theta$ = cot $\theta$ + 5 cosec $\theta$

Substituting the value of cot $\theta$ and cosec $\theta$ we get

6× $\frac{cos\theta}{sin\theta}$ + 2 × $\frac{1}{sin\theta}$ = $\frac{cos\theta}{sin\theta}$  + 5× $\frac{1}{sin\theta}$

$\frac{6cos\theta + 2}{sin\theta}$ = $\frac{cos\theta+5}{sin\theta}$

Since the denominators are equal,

6cos $\theta$ + 2 = cos $\theta$+5

6cos $\theta$ - cos $\theta$ = 5-2

5cos $\theta$ = 3

cos $\theta$ = $\frac{3}{5}$

The value of cos $\theta$ = $\frac{3}{5}$

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