Is 7cos^2(B)-7sin^2(B)=14cos^2(B)-7 ?

The answer to whether 7cos^2(B)-7sin^2(B)=14cos^2(B)-7 is True

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prove 7cos^2(B)-7sin^2(B)=14cos^2(B)-7

prove

7 cos^{2} (B) - 7 sin^{2} (B) = 14 cos^{2} (B) - 7

True

Solution steps

7 cos^{2} (B) - 7 sin^{2} (B) = 14 cos^{2} (B) - 7

Manipulating left side

7 cos^{2} (B) - 7 sin^{2} (B)

Rewrite using trig identities

7 cos^{2} (B) - 7 sin^{2} (B)

Use the Pythagorean identity:

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

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

= 7 cos^{2} (B) - 7 (1 - cos^{2} (B))

Simplify

7 cos^{2} (B) - 7 (1 - cos^{2} (B)) : 14 cos^{2} (B) - 7

7 cos^{2} (B) - 7 (1 - cos^{2} (B))

Expand

- 7 (1 - cos^{2} (B)) : - 7 + 7 cos^{2} (B)

- 7 (1 - cos^{2} (B))

Apply the distributive law:

a (b - c) = ab - a c

a = - 7, b = 1, c = cos^{2} (B)

= - 7 \cdot 1 - (- 7) cos^{2} (B)

Apply minus-plus rules

- (- a) = a

= - 7 \cdot 1 + 7 cos^{2} (B)

Multiply the numbers:

7 \cdot 1 = 7

= - 7 + 7 cos^{2} (B)

= 7 cos^{2} (B) - 7 + 7 cos^{2} (B)

Simplify

7 cos^{2} (B) - 7 + 7 cos^{2} (B) : 14 cos^{2} (B) - 7

7 cos^{2} (B) - 7 + 7 cos^{2} (B)

Group like terms

= 7 cos^{2} (B) + 7 cos^{2} (B) - 7

Add similar elements:

7 cos^{2} (B) + 7 cos^{2} (B) = 14 cos^{2} (B)

= 14 cos^{2} (B) - 7

= 14 cos^{2} (B) - 7

= 14 cos^{2} (B) - 7

= 14 cos^{2} (B) - 7

We showed that the two sides could take the same form

\Rightarrow True

sec^{2} (x) (sec (x) - cos (x)) = tan^{2} (x)

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

1 - \frac{sin ( x )}{1 + cos ( x )} = cos (x)

2 cos (3 x) = cot (3 x)

cos^{2} (θ) tan^{2} (θ) + cos^{2} (θ) = 1

Is 7cos^2(B)-7sin^2(B)=14cos^2(B)-7 ?
The answer to whether 7cos^2(B)-7sin^2(B)=14cos^2(B)-7 is True