Is tan(a)sin(a)+cos(a)=sec(a) ?

The answer to whether tan(a)sin(a)+cos(a)=sec(a) is True

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prove tan(a)sin(a)+cos(a)=sec(a)

prove

tan (a) sin (a) + cos (a) = sec (a)

True

Solution steps

tan (a) sin (a) + cos (a) = sec (a)

Manipulating left side

tan (a) sin (a) + cos (a)

Express with sin, cos

= \frac{cos ^{2} ( a ) + sin ^{2} ( a )}{cos ( a )}

Rewrite using trig identities

= \frac{1}{cos ( a )}

Rewrite using trig identities

sec (a)

We showed that the two sides could take the same form

\Rightarrow True

sin (\frac{3 π}{4}) = sin (\frac{3}{4} π + 2 π)

\frac{cos ( θ ) + cos ( 3 θ )}{2 cos ( θ )} = cos (2 θ)

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

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

3 tan (x) = 4 sin (x)

Is tan(a)sin(a)+cos(a)=sec(a) ?
The answer to whether tan(a)sin(a)+cos(a)=sec(a) is True