Is 7csc^2(x)-5cot^2(x)=2csc^2(x)+5 ?

The answer to whether 7csc^2(x)-5cot^2(x)=2csc^2(x)+5 is True

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prove 7csc^2(x)-5cot^2(x)=2csc^2(x)+5

prove

7 csc^{2} (x) - 5 cot^{2} (x) = 2 csc^{2} (x) + 5

True

Solution steps

7 csc^{2} (x) - 5 cot^{2} (x) = 2 csc^{2} (x) + 5

Manipulating left side

7 csc^{2} (x) - 5 cot^{2} (x)

Rewrite using trig identities

= 2 csc^{2} (x) + 5

We showed that the two sides could take the same form

\Rightarrow True

cos^{2} (x) (1 + cot^{2} (x)) = cot^{2} (x)

\frac{1}{csc ( x ) + cot ( x )} = csc (x) - cot (x)

tan (θ) (cot (θ) + tan (θ)) = sec^{2} (θ)

sec^{2} (- θ) - 1 = tan^{2} (θ)

2 tan (x) = \frac{cos ( x )}{csc ( x ) - 1} + \frac{cos ( x )}{csc ( x ) + 1}

Is 7csc^2(x)-5cot^2(x)=2csc^2(x)+5 ?
The answer to whether 7csc^2(x)-5cot^2(x)=2csc^2(x)+5 is True