Simplify cotx 1 2cos2 xsin x cos xSolutioncotx 12cos2xsin

Simplify cotx + 1 - 2cos^2 x/sin x cos x

Solution

cotx + (1-2cos²x)/(sinxcosx)

=[(sinxcosx)cotx + (1-2cos²x)]/(sinxcosx)

write cot x as cosx /sinx

=[(sinxcosx)(cosx/sinx) + (1-2cos²x)]/(sinxcosx)

=[cos²x + (1-2cos²x)]/(sinxcosx)

=[ (1-cos²x)]/(sinxcosx)

=[ sin²x]/(sinxcosx)

=(sinxsinx)/(sinxcosx)

=tanx

cotx + (1-2cos²x)/(sinxcosx) =tanx