Prove: `sin θ(1 + tan θ) + cos θ(1 + cot θ) = (sec θ + cosec θ)`.

Answer

D

Explanation

a. Area of `DeltaADB = (1)/(2) AD xx BD`
`= (1)/(2) c sin B xx c cos B`
`= (c^(2))/(4) sin 2B`
b. Area of `DeltaADC = (1)/(2) AD xx CD`
`= (1)/(2) b sin C xx b cos C = (b^(2))/(4) sin 2C`
c. Area of `DeltaADE = (1)/(2) AE xx DE`
`= (1)/(2) AD cos ((pi)/(2) - B) AD sin ((pi)/(2) - B)`
`= (1)/(4) AD^(2) sin 2B`
`= (1)/(4) c^(2) sin^(2) B sin 2B`
d. Area of `DeltaBDE = (1)/(2) BE xx DE`
`= (1)/(2) BD cos B xx AD sin ((pi)/(2) -B)`
`= (1)/(2) c cos B cos B xx c sin B cos B`
`= (1)/(4) c^(2) cos^(2) B sin 2B`