Question

1/coseca_cota=coseca+cota

Answer 1

Given :

• $\sf{\dfrac{1}{coseca - cota}}$

To Prove :

• $\sf{\dfrac{1}{coseca - cota} = cosec a + cot a}$

Solution :

$\underline{\boxed { \blue{\sf{LHS}}}} = \sf \pink{\dfrac{1}{coseca - cota}} \\ \\ \\ \implies{\sf{ \purple{\dfrac{1}{coseca - cota} \times \sf\dfrac{coseca + cota}{coseca + cota}}}} \\ \\ \\ \implies {\sf{ \green{ \dfrac{cosec a + cot a}{cosec^{2}a - cot^{2} a }}}} \\ \\ \\ \implies {\sf{\orange{cosec a + cot a}}}=\underline{\boxed{\sf {\red{ RHS}}}}$

Addition information :

• 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

• sinø = Cos(90° - ø)

• cosø= sin(90° - ø)

• tanø = cot(90° - ø)

• cotø = tan(90° - ø)

• secø = cosec(90° - ø)