SOLUTION: how do i write tan 25 + tan 5 / 1 - tan 25 tan 5 as the sine, cosine or tangent of an angle?
And how do i find the exact value
Please help show the steps
thank you
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-> SOLUTION: how do i write tan 25 + tan 5 / 1 - tan 25 tan 5 as the sine, cosine or tangent of an angle?
And how do i find the exact value
Please help show the steps
thank you
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Question 919192: how do i write tan 25 + tan 5 / 1 - tan 25 tan 5 as the sine, cosine or tangent of an angle?
And how do i find the exact value
Please help show the steps
You can put this solution on YOUR website! Search your table of trig identities to find
(1) tan(x+y) = (tan(x) + tan(y))/(1-tan(x)*tan(y))
Use your problem with x = 25 and y = 5, we get
(2) tan(30) = (tan(25) + tan(5))/(1-tan(25)*tan(5))
Answer: The trig expression is tan(30).
Proof that
(3) tan(x+y) = (tan(x) + tan(y))/(1-tan(x)*tan(y))
is as follows:
(4) tan(x+y) = sin(x+y)/cos(x+y) or using sin and cos of sums gives
(5) tan(x+y) = (sin(x)cos(y)+cos(x)sin(y))/(cos(x)cos(y)-sin(x)sin(y))
Now divide all four terms of (5) by cos(x)cos(y) and get
(6) tan(x+y) = (tan(x)+ tan(y))/(1-tan(x)tan(y)) QED
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