If tan (A+B)=p, tan (A−B)=q,tan (𝐴+𝐵)=𝑝, tan (𝐴−𝐵)=𝑞, then the value of tan2A in terms of p and q is
Question
Solution
To find the value of tan2A in terms of p and q, we can use the formula for tan(A+B) and tan(A-B) and the formula for tan2A.
The formula for tan(A+B) is (tanA + tanB) / (1 - tanAtanB) and the formula for tan(A-B) is (tanA - tanB) / (1 + tanAtanB).
Given that tan(A+B) = p and tan(A-B) = q, we can write:
p = (tanA + tanB) / (1 - tanA*tanB) ----(1)
q = (tanA - tanB) / (1 + tanA*tanB) ----(2)
We can solve these two equations to find the values of tanA and tanB.
Next, we use the formula for tan2A, which is 2*tanA / (1 - tan^2A).
Substitute the values of tanA and tanB from equations (1) and (2) into the formula for tan2A to get the value of tan2A in terms of p and q.
After solving these equations, we get:
tan2A = (2*(p+q)) / (1 - p*q)
So, the value of tan2A in terms of p and q is (2*(p+q)) / (1 - p*q).
Similar Questions
If tan (A+B)=p, tan (A−B)=q,tan (𝐴+𝐵)=𝑝, tan (𝐴−𝐵)=𝑞, then the value of tan2A in terms of p and q is
In a triangle PQR,∠R=π2, if tan(P2) and tan(Q2)𝑃𝑄𝑅,∠𝑅=𝜋2, if tan(𝑃2) and tan(𝑄2) are the roots of the equation ax2+bx+c=0(a≠0)𝑎𝑥2+𝑏𝑥+𝑐=0(𝑎≠0) then
If tan(α) = 512512 and sin(β) = 3535, where α and β are acute angles, calculate the value of tan(α - β).
If the angles of A, B and C of a ΔABC are in A.P. and the sides a, b and c opposite to these angles are in G.P., then a2, b2 and c2 are in –
If in ∆ ABC and ∆ PQR, ொோ = ோ = ொ then:a) ∆PQR ~∆CAB b) ∆PQR ~∆ABC c) ∆CBA ~∆PQR d) ∆BCA ~∆PQR
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.