Question 1097306: Simplify: sinβ secβ + cosβ cscβ
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! sec beta=1/cos beta; csc beta=1/sin beta
therefore sin beta*sec beta=sin beta/cos beta=tan beta.
cos beta*csc beta,
cos beta*csc beta= cos beta/ sin beta=ctn beta
The sum is sin beta/cos beta+ cos beta/sin beta.
common denominator of sin beta* cos beta
Numerator becomes sin^2 beta+cos^2 beta=1
Therefore, the sum is 1/sin beta*cos beta ANSWER
Check
Let beta=30 degrees
sin beta*sec beta=0.5774, same as tan 30
cos beta*csc beta=1.732, same as ctn 30. Their sum is 2.31
(1/2)*2/sqrt(3) is first term=1/sqrt (3)
sqrt(3)/2*2= sqrt(3) is the second term. The sum is sqrt(3)+1/sqrt(3)=2.31
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