SOLUTION: Simplify (cos (𝜃 +3𝜋/2) csc(5𝜋 + 𝜃))/ (tan (𝜃 −𝜋/2) sin(−2𝜃)) into an expression which involves only one trigonometric function.

Algebra ->  Trigonometry-basics -> SOLUTION: Simplify (cos (𝜃 +3𝜋/2) csc(5𝜋 + 𝜃))/ (tan (𝜃 −𝜋/2) sin(−2𝜃)) into an expression which involves only one trigonometric function.      Log On


   

Question 1204326: Simplify
(cos (𝜃 +3𝜋/2) csc(5𝜋 + 𝜃))/
(tan (𝜃 −𝜋/2) sin(−2𝜃))
into an expression which involves only one trigonometric function.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

1.


use
cos+%28theta+%2B3pi%2F2%29=sin%28theta%29
csc%285pi+%2B+theta%29=-csc%28theta%29
tan%28theta+%29+%2A%28-csc%282+theta+%29%29=-cot%28theta%29
sin%28-2theta%29=+-sin%282theta%29





since
sin%28theta%29%2A%28-csc%28theta%29%29=-1

then we have

1%2F%28-cot%28theta%29%2A%28-sin%282theta%29%29%29

-1%2F%28sin%282theta%29%2A+cot%28theta%29%29

-%281%2Fsin%282theta%29%29%2A%281%2F+cot%28theta%29%29

-%28csc%282theta%29%2Atan%28theta%29+%29

-csc%282theta%29%2Atan%28theta%29+

2.
%28tan%28theta+-pi%2F2%29+%2Asin%28-2theta%29%29
since:
tan+%28theta-pi%2F2%29=-cot%28theta%29
sin%28-2theta%29=+-sin%282theta%29

then we have
-cot%28theta%29+%2A%28-sin%282theta%29%29
cot%28theta%29+%2Asin%282theta%29