Question

If cosA=2cosB then, find tan(A-B /2) tan(A+B/2) ??
Here A= theta 1
B= theta2

Answer 1

Step-by-step explanation:

cosa/cosb = k

(cos b – cos a)/(cos b + cos a) = (1-k) / (1+k)

[sin ((a-b)/2)sin((a+b)/2)]/ [cos ((a-b)/2)cos((a+b)/2)] = (1-k) / (1+k)

[tan ((a-b)/2)tan((a+b)/2)] = (1-k) / (1+k)

tan((a+b)/2) = [(1-k) / (1+k)] cot ((a-b)/2)

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Answer 2

cosa/cosb = k

(cos b – cos a)/(cos b + cos a) = (1-k) / (1+k)

[sin ((a-b)/2)sin((a+b)/2)]/ [cos ((a-b)/2)cos((a+b)/2)] = (1-k) / (1+k)

[tan ((a-b)/2)tan((a+b)/2)] = (1-k) / (1+k)

tan((a+b)/2) = [(1-k) / (1+k)] cot ((a-b)/2)

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