Example 12

Transcript

Example 12 Simplify tan-1 [(a cos⁡〖x −b sin⁡x 〗)/(b cos⁡〖x+a sin⁡x 〗 )], if a/b tan x > -1 tan-1 [(a cos⁡〖x − b sin⁡x 〗)/(b cos⁡〖x + a sin⁡x 〗 )] = tan-1 [((a cos⁡〖x − b sin⁡x 〗)/(b cos⁡x ))/((b cos⁡〖x + a sin⁡x 〗)/(b cos⁡x ))] = tan-1 [((𝑎 cos⁡𝑥)/(𝑏 cos⁡𝑥 ) − (𝑏 sin⁡𝑥)/(𝑏 cos⁡𝑥 ))/((𝑏 cos⁡𝑥)/(𝑏 cos⁡𝑥 ) + (𝑎 sin⁡𝑥)/(𝑏 cos⁡𝑥 ))] = tan-1 [(𝑎/(𝑏 ) − (𝑏 sin⁡𝑥)/(𝑏 cos⁡𝑥 ))/(1 + (𝑎 sin⁡𝑥)/(𝑏 cos⁡𝑥 ))] = tan-1 [(a/b − tan⁡x)/(1 + a/b tan⁡x )] = tan-1 a/b – tan-1 (tan x) = tan-1 a/b − x