Is prove-sin^2(x)sec^2(x)=1-sec^2(x) ?

The answer to whether prove-sin^2(x)sec^2(x)=1-sec^2(x) is True

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prove-sin^2(x)sec^2(x)=1-sec^2(x)

prove

- sin^{2} (x) sec^{2} (x) = 1 - sec^{2} (x)

True

Solution steps

- sin^{2} (x) sec^{2} (x) = 1 - sec^{2} (x)

Manipulating left side

- sin^{2} (x) sec^{2} (x)

Rewrite using trig identities

= - (1 - cos^{2} (x)) (tan^{2} (x) + 1)

Expand

- (1 + tan^{2} (x)) (1 - cos^{2} (x)) : - 1 + cos^{2} (x) - tan^{2} (x) + tan^{2} (x) cos^{2} (x)

= - 1 + cos^{2} (x) - tan^{2} (x) + cos^{2} (x) tan^{2} (x)

Rewrite using trig identities

= 1 - sec^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1}{1 + cos ^{2} ( x )} + \frac{1}{1 + sec ^{2} ( x )} = 1

sin^{2} (θ) + sin^{2} (θ) tan^{2} (θ) = tan^{2} (θ)

1 + sin (2 θ) = (cos (θ) sin (θ))^{2}

sec (θ) csc (θ) = tan (θ) + cot (θ)

2 tan (0^{\circ}) = sin (0^{\circ})

Is prove-sin^2(x)sec^2(x)=1-sec^2(x) ?
The answer to whether prove-sin^2(x)sec^2(x)=1-sec^2(x) is True