Is 3+5sin^2(a)=8-5cos^2(a) ?

The answer to whether 3+5sin^2(a)=8-5cos^2(a) is True

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prove 3+5sin^2(a)=8-5cos^2(a)

prove

3 + 5 sin^{2} (a) = 8 - 5 cos^{2} (a)

True

Solution steps

3 + 5 sin^{2} (a) = 8 - 5 cos^{2} (a)

Manipulating left side

3 + 5 sin^{2} (a)

Rewrite using trig identities

3 + 5 sin^{2} (a)

Use the Pythagorean identity:

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

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

= 3 + 5 (1 - cos^{2} (a))

Simplify

3 + 5 (1 - cos^{2} (a)) : - 5 cos^{2} (a) + 8

3 + 5 (1 - cos^{2} (a))

Expand

5 (1 - cos^{2} (a)) : 5 - 5 cos^{2} (a)

5 (1 - cos^{2} (a))

Apply the distributive law:

a (b - c) = ab - a c

a = 5, b = 1, c = cos^{2} (a)

= 5 \cdot 1 - 5 cos^{2} (a)

Multiply the numbers:

5 \cdot 1 = 5

= 5 - 5 cos^{2} (a)

= 3 + 5 - 5 cos^{2} (a)

Add the numbers:

3 + 5 = 8

= - 5 cos^{2} (a) + 8

= - 5 cos^{2} (a) + 8

= - 5 cos^{2} (a) + 8

= 8 - 5 cos^{2} (a)

We showed that the two sides could take the same form

\Rightarrow True

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

(1 + tan (β)) (1 - tan (β)) = 2 - sec^{2} (β)

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

cos^{2} (x) - cos^{2} (9 0^{\circ} - x) = 1 - 2 sin (x)

sec^{2} (t) csc^{2} (t) = sec^{2} (t) + csc^{2} (t)

Is 3+5sin^2(a)=8-5cos^2(a) ?
The answer to whether 3+5sin^2(a)=8-5cos^2(a) is True