Is sin(a)sec(a)tan(a)+1=sec^2(a) ?

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

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prove sin(a)sec(a)tan(a)+1=sec^2(a)

prove

sin (a) sec (a) tan (a) + 1 = sec^{2} (a)

True

Solution steps

sin (a) sec (a) tan (a) + 1 = sec^{2} (a)

Manipulating left side

sin (a) sec (a) tan (a) + 1

Rewrite using trig identities

sin (a) sec (a) tan (a) + 1

Express with sin, cos

sec (a) sin (a)

Use the basic trigonometric identity:

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

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

Simplify

\frac{1}{cos ( a )} sin (a) : \frac{sin ( a )}{cos ( a )}

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Multiply:

1 \cdot sin (a) = sin (a)

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

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

= 1 + \frac{sin ( a )}{cos ( a )} tan (a)

Use the basic trigonometric identity:

\frac{sin ( a )}{cos ( a )} = tan (a)

= 1 + tan (a) tan (a)

tan (a) tan (a) = tan^{2} (a)

tan (a) tan (a)

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

tan (a) tan (a) = tan^{1 + 1} (a)

= tan^{1 + 1} (a)

Add the numbers:

1 + 1 = 2

= tan^{2} (a)

= 1 + tan^{2} (a)

Use the Pythagorean identity:

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

= sec^{2} (a)

= sec^{2} (a)

We showed that the two sides could take the same form

\Rightarrow True

\frac{tan ( y ) + cot ( y )}{csc ( y )} = sec (y)

\frac{sec ^{2} ( a ) - 1}{sec ^{2} ( a )} = sin^{2} (a)

\frac{1}{sec ( x )} = sec (x) - tan (x) \cdot sin (x)

2 sin^{2} (x) - sin (x) - 1 = 0

2 cos^{2} (θ) - 1 = cos (2 θ)

Is sin(a)sec(a)tan(a)+1=sec^2(a) ?
The answer to whether sin(a)sec(a)tan(a)+1=sec^2(a) is True