Question

Using sums and differences, calculate:

a) cos 15
b) cotg 165
c) cossec 15

Answer 1

in steps

Explanation:

cos 15° = cos (45° - 30°) = cos 45° cos 30° + sin 45° sin 30°

= (√2 / 2) (√3 / 2) + (√2 / 2) (1 / 2)

= (√3/2√2) + (1/2√2)

= (√3 + 1) / 2√2 (0.9659)

cot 165° = cot (90° + 75°) = - tan 75° = - (2 + √3)

csc 15° = 1 / sin 15° = 1 / sin (45° - 30°)

= 1 / (sin 45° cos 30° - cos 45° sin 30°)

= 1 / ( √2/2 x √3/2 - √2/2 x 1/2)

= 1 / ((√6 - √2) / 4)

= 4 / (√6 - √2)

=√6 + √2