Question

Evaluate : sec 840°cot(-945degree) + sin 1770°.​

Answer 1

Evaluate : sec 840° * cot(-945°) + sin 1770°.

Solution :-

Lets Solve them separately :-

a) sec 840°

→ sec 840°

→ sec (720° + 120°)

→ sec (2*360° + 120°)

→ sec (120°)

→ sec (90° + 30°)

using sec (90° + A) = - (cosec A)

→ - (cosec 30°)

using value of cosec 30° = 2

→ (-2) .

b) cot(-945°)

→ cot(-945°)

→ (-1) * cot(945°)

→ (-1) * cot(720° + 225°)

→ (-1) * cot(225°)

→ (-1) * cot(180° + 45°)

using cot(180° + A) = cotA

→ (-1) * cot 45°

→ (-1) * 1

→ (-1) .

C) sin (1770°)

→ sin 1770°

→ sin(1800° - 30°)

→ sin(5*360° - 30°)

in 4th Quadrant , sin(360° - A) = - sinA

→ - sin30°

→ (-1/2).

Therefore,

→ sec 840° * cot(-945°) + sin 1770°.

→ (-2) * (-1) + (-1/2)

→ 2 + (-1/2)

→ 2 - (1/2)

→ (4 - 1)/2

→ (3/2) (Ans.)