Question

Simplify: sin³Ф+cos³Ф/sinФ+cosФ + sinФcosФ

Answer 1

Given :

sin³Ф+cos³Ф/sinФ+cosФ + sinФcosФ

To find :

• simplify

Solution :

As A,B and C arc the interior angles of ΔABC,

➵ A + B + C = 180°

➵ B + C = 180° - A

➵ B + C = 90° - A/2..........(I)

➵ Now, sin B + C/2

➵ sin(90° - A/2) (using (i))

➵ sin B + C/2

➵ cos A/2 ( sin (90°- ø) = cos ø. )

Extra information :

• sinø = Cos(90° - ø)

• cos6= sin(90° - ø)

• tanø = cot(90° - ø)

• cotø = tan(90° - ø)

• secø = cosec(90° - ø)

• tanø = sinø/cosø

• secø = 1/cosø

• cotø = 1/tanø = sinø/cosø

• 1 - tan(ø/2)/1 - tan(ø/2) = ±√1 - sinø/1 + sinø

• tan ø/2 = ±√1 - cosø/1 + cosø