What is the general solution for cos(x+25)sec(65-x)=1 ?

The general solution for cos(x+25)sec(65-x)=1 is x=20-180n

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cos(x+25)sec(65-x)=1

cos (x + 2 5^{\circ}) sec (6 5^{\circ} - x) = 1

x = 2 0^{\circ} - 18 0^{\circ} n

Solution steps

cos (x + 2 5^{\circ}) sec (6 5^{\circ} - x) = 1

Subtract

1

from both sides

cos (x + 2 5^{\circ}) sec (6 5^{\circ} - x) - 1 = 0

Simplify

cos (x + 2 5^{\circ}) sec (6 5^{\circ} - x) - 1 : cos (\frac{36 x + 90 0 ^{\circ}}{36}) sec (\frac{234 0 ^{\circ} - 36 x}{36}) - 1

cos (\frac{36 x + 90 0 ^{\circ}}{36}) sec (\frac{234 0 ^{\circ} - 36 x}{36}) - 1 = 0

Rewrite using trig identities

- 1 + tan (\frac{234 0 ^{\circ} - 36 x}{36}) = 0

Move

1

to the right side

tan (\frac{234 0 ^{\circ} - 36 x}{36}) = 1

General solutions for

tan (\frac{234 0 ^{\circ} - 36 x}{36}) = 1

\frac{234 0 ^{\circ} - 36 x}{36} = 4 5^{\circ} + 18 0^{\circ} n

Solve

\frac{234 0 ^{\circ} - 36 x}{36} = 4 5^{\circ} + 18 0^{\circ} n : x = 2 0^{\circ} - 18 0^{\circ} n

x = 2 0^{\circ} - 18 0^{\circ} n

2 cos^{2} (x) = 3 (sin (x) + 1)

cos^{2} (θ) = \frac{2 + 3}{4}

x, cos (x) = sin (x + y)

2 cos (5 x) = 9

- 5 cos (c) - 1 = 2 cos (c) + 3

What is the general solution for cos(x+25)sec(65-x)=1 ?
The general solution for cos(x+25)sec(65-x)=1 is x=20-180n