If A + B + C = π 2 thrn prove that: tan ⁡ (...

babyagelesszj

babyagelesszj

Answered

2022-07-01

If A + B + C = π 2 thrn prove that:
tan ( A + B ) [ tan A tan B ] = 1 + cot 2 C ( sec A cos B cos A sec B )

Answer & Explanation

Janiyah Patton

Janiyah Patton

Expert

2022-07-02Added 12 answers

Here,
A + B + C = π 2
A + B = π 2 C
Now,
L . H . S . = tan ( A + B ) [ tan A tan B ] = tan ( π 2 C ) ( sin A cos A sin B cos B )
cot C sin ( A B ) cos A cos B = cos C sin C sin ( A B ) cos A cos B = sin ( A + B ) cos ( A + B ) sin ( A B ) cos A cos B = cos 2 B cos 2 A 2 sin C ( cos A cos B ) = cos 2 B cos 2 A sin C cos A cos B = 1 sin C ( sec A cos B cos A sec B ) = cosec  C ( sec A cos B cos A sec B ) = 1 + cot 2 C ( sec A cos B cos A sec B )

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