SOLUTION: Evaluate the following expression. sin(90°-θ)*tan(θ)*sec(θ) A) sin(θ) B) cos(θ) C) tan(θ) D) cot(θ)

Algebra.Com
Question 1058831: Evaluate the following expression.
sin(90°-θ)*tan(θ)*sec(θ)
A) sin(θ)
B) cos(θ)
C) tan(θ)
D) cot(θ)
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
Evaluate the following expression.
sin(90°-θ)*tan(θ)*sec(θ)
A) sin(θ)
B) cos(θ)
C) tan(θ)
D) cot(θ)

The word "cosine", "CO SINE", is an abbreviation for COmplement's SINe.

90°-θ is the COmplement of θ, so sin(90°-θ) is the 
COmplement of θ's SINe, so 

sin(90°-θ) equals cos(θ).

Therefore:

sin(90°-θ)*tan(θ)*sec(θ) = 

cos(θ)*tan(θ)*sec(θ) =

Use reciprocal identity for sec(θ):




 


Edwin
RELATED QUESTIONS

The expression sin θ (cot θ - csc θ) is equivalent to? A) 2 Cos θ (answered by stanbon,lynnlo)
Which expression is equivalent to sin θ + cos θ cot θ? The choices are:... (answered by Alan3354)
Verify:... (answered by lwsshak3)
Find an expression equivalent to (secθ tanθ/sinθ) A. sec^2θ B.... (answered by Fombitz)
If tanθ = 5/12 and sinθ < 0 , evaluate a) sinθ b) cosθ c)... (answered by math-vortex)
If tanθ = 5/12 and sinθ < 0 ,evaluate a) sinθ b) cosθ c)... (answered by lwsshak3)
Which of the following is a trigonometric identity? a. cot θ + tan θ = 1 b.... (answered by ikleyn,fractalier)
Which of the following is a trigonometric identity? a. cot θ + tan θ = 1 b.... (answered by fractalier,ikleyn)
Prove. sinēθ + tanēθ +cosēθ =... (answered by Edwin McCravy)