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Prove:

(i) 2tan-1 (3/4) – tan-1 (17/31) = π/4

(ii) 2tan-1 (1/2) + tan-1 (1/7) = tan-1 (31/17)

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Best answer

(i) Given as 2tan-1(3/4) – tan-1(17/31) = π/4

Considering L.H.S.

= 2tan-1(3/4) - tan-1(17/31)

As we know that

= tan-1(625/625)

= tan-1 (1)

= π/4 = R.H.S.

Therefore, 2tan-1(3/4) - tan-1(17/31) = π/4

Hence, proved

(ii) Given as 2tan-1(1/2) + tan-1(1/7) = tan-1(31/17)

Considering L.H.S.

= 2tan-1(1/2) + tan-1(1/7)

As we know 

= R.H.S.

Therefore, 2tan-1(1/2) + tan-1(1/7) = tan-1(31/17)

Hence, proved

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