If it is given tan(A-B)
tanA-tanB/-1+tanAtanB and tanP-1/1+tanP=tan195
Find the value of P
To find the value of P in the equation tanP - 1 / 1 + tanP = tan195, we can use the trigonometric identity tan(A-B) = (tanA - tanB) / (1 + tanA*tanB).
Comparing the given equation with the trigonometric identity, we can see that tanA = tanP and tanB = 1.
So, we can rewrite the equation as tanA - tanB / 1 + tanA*tanB = tan195.
Substituting tanA = tanP and tanB = 1, we get tanP - 1 / 1 + tanP*1 = tan195.
Simplifying the equation, we get tanP - 1 / 1 + tanP = tan195.
Now, let's solve for P using the equation.
First, multiply both sides of the equation by (1 + tanP) to eliminate the denominator:
(1 + tanP)*(tanP - 1) / (1 + tanP) = tan195*(1 + tanP).
Expanding the equation, we get:
tanP - 1 + tanP*tanP - tanP = tan195 + tan195*tanP.
Simplifying further:
2tanP*tanP - 2tanP - tan195*tanP - tanP + 1 - tan195 = 0.
Rearranging the equation, we get:
2tanP*tanP - tanP - (2 + tan195)*tanP + (1 - tan195) = 0.
Now, solve this quadratic equation to find the values of tanP.
We can solve this equation by factoring, completing the square, or using the quadratic formula.
Once you find the values of tanP, you can use the inverse tangent function (arctan or tan^(-1)) to find the value of P.
I hope this helps you in finding the value of P!