Question

if sin@ + cosec@ =√3 prove that Sin^2@+cosec^2@=1​

Answer 1

Given :

• sin A + cosec A = √3

To prove :

• sin²A + cosec²A = 1

Proof :

As given

→ sin A + cosec A = √3

squaring both sides

→ ( sin A + cosec A )² = ( √3 )²

using algebraic identity

( a + b )² = a² + b² + 2 a b

→ sin²A + cosec²A + 2 sin A cosec A = 3

putting cosec A = 1 / sin A

→ sin²A + cosec²A + 2 sin A ( 1 / sin A ) = 3

→ sin²A + cosec²A + 2 = 3

→ sin²A + cosec²A = 3 - 2

→ sin²A + cosec²A = 1

Proved .

Trigonometric ratios and identities to know :

__________________________

→  Cos² θ + Sin² θ = 1

→ 1 + Tan² θ = Sec² θ

→ 1 + Cot² θ = Cosec² θ

__________________________

→  sin ( 90 - A ) = cos A

→ cos ( 90 - A ) = sin A

→ tan ( 90 - A ) = cot A

→ cot ( 90 - A ) = tan A

→  sec ( 90 - A ) = cosec A

→ cosec ( 90 - A ) = sec A

__________________________

→  cosec A = 1 / sin A

→  sec A = 1 / cos A

→  tan A = 1  / cot A = sin A / cos A

→ cot A = 1 / tan A = cos A / sin A

__________________________

Answer 2

Answer:

SinA+cosecA=v3 is impossible

SinA+cosec A greater than or equal to 2