In PQR ang R pi 2 If tan P 2 and tan Q 2 are the roots of the equation ax2 bx nb...........

Mathematics (NDA) Trigonometry

In ?PQR, ∠R = π / 2 . If tan ( P / 2 ) and tan ( Q / 2 ) are the roots of the equation ax² = bx +c = 0, then which one of the following is correct?

a = b + c

b = c + a

c = a + b

b = c

R = π / 2 ∴ P + Q = π / 2 [sum of angles of a triangle = π ]

P / 2 + Q / 2 = π / 4

tan ( P / 2 + Q / 2 ) = π / 4

tan P / 2 + tan Q / 2 / 1−tan P / 2 tan Q / 2 = tan π / 4 →(1)

Now tan P/ 2 and tan Q / 2 are roots of equation a x² + b x + c = 0

∴ Sum of roots = -b/a

And product of roots = c/a

Putting in (1):

−b/a / 1−c/a = 1

Or a + b = c

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