Solve this: MATLIEM,VITCS
cos (Tt + r)
— — cos r
cos (27t — x)
cos x
sin (ß + x) — — sin x
sin (27t — x)
Similar results [Or tan x, cot x, see x and eoscw x can be obtained from the results Of sin
x and Cos
10.
If none of the angles x, y and (x •v y) is an odd multiple of — , then
tan x + tan y
tan (x + y) = I
— tan x tan y
Since none of the x, y and (x + y) is an odd multiple Of —
cos y and cos (x + y) are non-zero Now
it follows that eos x,
sin(x + y)
sin x cosy cosxsin y
tan (x + y) —
cos(x + y) cosx y — sin x sin y
Dividing numerator and denominator hy cos x cos y, we have
sin x cos y
cos x cos
tan (x y) ¯
cosx cos y
cosx cos y
COSxSln y
cosxcos v
cos x cos y
tan + tan y
I — Ian x Ian y
tan x — tan y
tan ( r
I + tan x tan y
If we replace y by—y In Identity I O. we get
tan (x — y) — tan [s + y)]
tan x + tan
I —tan x tan
tan x — tan y
I + tan x tan y
If none of the angles x, y and (x + y) is a multiple of N, then
cot x cot y —I
cot (x + y) ¯
eut y + cot x
