Question

X Cot (90+theta) + Tan (90+theta) Sin theta + Cosec (90+theta) = 0 ......then find the value of X

Answer 1

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Answer 2

Answer:

The value of x is sinθ

Step-by-step explanation:

Step 1:

Given Data:

X Cot (90+theta) + Tan (90+theta) Sin theta + Cosec (90+theta) = 0.

To find the value of X  

Step 2:

Xcot(90+θ)+tan(90+θ)sinθ+cosec(90+θ)=0

X(-tanθ)+(-cotθ)sinθ+secθ=0

Step 3:

-xtanθ- cotθsinθ+secθ=0

Step 4:

-xtanθ- cosθ/sin θ x sinθ+ secθ=0 (Cancel sinθ)

-xtanθ- cosθ + secθ=0

Step 4:

-xsinθ/cosθ-cosθ+1/cosθ=0

$-\mathrm{x} \sin \theta-\cos ^{2} \theta+1 / \cos \theta=0$

Step 5:

$-x \sin \theta-\cos ^{2} \theta+1=0$

$\left.-x \sin \theta+1-\cos ^{2} \theta=0 \quad \text { (therefore } 1-\cos ^{2} \theta=\sin ^{2} \theta\right)$

Step 6:

$-x \sin \theta=-\sin ^{2} \theta$ (cancel minus sign on both sides)

X=sinθ