What is the general solution for tan(A/2)=sqrt(1.02) ?

The general solution for tan(A/2)=sqrt(1.02) is A=2*0.79034…+2pin

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tan(A/2)=sqrt(1.02)

tan (\frac{A}{2}) = 1.02

A = 2 \cdot 0.79034 \dots + 2 πn

Degrees

A = 90.56729 \dots^{\circ} + 36 0^{\circ} n

Solution steps

tan (\frac{A}{2}) = 1.02

Apply trig inverse properties

tan (\frac{A}{2}) = 1.02

General solutions for

tan (\frac{A}{2}) = 1.02

tan (x) = a \Rightarrow x = arctan (a) + πn

\frac{A}{2} = arctan (1.02) + πn

\frac{A}{2} = arctan (1.02) + πn

Solve

\frac{A}{2} = arctan (1.02) + πn : A = 2 arctan (1.02) + 2 πn

\frac{A}{2} = arctan (1.02) + πn

Multiply both sides by

2

\frac{A}{2} = arctan (1.02) + πn

Multiply both sides by

2

\frac{2 A}{2} = 2 arctan (1.02) + 2 πn

Simplify

A = 2 arctan (1.02) + 2 πn

A = 2 arctan (1.02) + 2 πn

A = 2 arctan (1.02) + 2 πn

Show solutions in decimal form

A = 2 \cdot 0.79034 \dots + 2 πn

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

h = 3 sin (2 x - 1) + 4

sin^{2} (x) + 2 = 3 sin (x)

sin (x + \frac{π}{3}) = \frac{1}{2} cos (x - \frac{π}{6})

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

What is the general solution for tan(A/2)=sqrt(1.02) ?
The general solution for tan(A/2)=sqrt(1.02) is A=2*0.79034…+2pin