Is 1+sec^2(x)=2+tan^2(x) ?

The answer to whether 1+sec^2(x)=2+tan^2(x) is True

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prove 1+sec^2(x)=2+tan^2(x)

prove

1 + sec^{2} (x) = 2 + tan^{2} (x)

True

Solution steps

1 + sec^{2} (x) = 2 + tan^{2} (x)

Manipulating left side

1 + sec^{2} (x)

Rewrite using trig identities

1 + sec^{2} (x)

Use the Pythagorean identity:

sec^{2} (x) = tan^{2} (x) + 1

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

Simplify

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

1 + tan^{2} (x) + 1

Group like terms

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

Add the numbers:

1 + 1 = 2

= tan^{2} (x) + 2

= tan^{2} (x) + 2

= tan^{2} (x) + 2

= 2 + tan^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

9 (1 + sin (y)) (1 + sin (- y)) = 9 cos^{2} (y)

(\frac{tan ( θ )}{sec ( θ )}) = sin (θ)

sin (4 5^{\circ}) cot (4 5^{\circ}) = cos (4 5^{\circ})

sec (4 x) = 2

\frac{1}{cos ^{2} ( A )} + \frac{1}{cot ^{2} ( A )} = 1