Question

Prove This
Everyone Please​

Answer 1

We have to prove LHS =RHS

Take LHS

1 /cosA+sinA-1 + 1/cosA+sinA+1

Take the LCM to the denominator

After taking Simplify it

In denominator It is in form of

( a + b ) ( a - b ) = a² - b²

Then simplify it

We get

2cosA + 2sinA / (cosA+sinA)² -1

Applied above formula

Then simplify it

In this process We have to know

sin²A + cos²A =1

After simplifying we get,

2cosA + 2sinA /2cosAsinA

Divide 2cosA sinA with each term

We get 1/sinA + 1/cosA

We know that,

1 / sinA = cosecA

1/ cosA = sec A

Then we get

1/sinA + 1/cosA = cosecA + secA

Hence proved !

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Know more :-

Trignometric Identities

sin²θ + cos²θ = 1

sec²θ - tan²θ = 1

csc²θ - cot²θ = 1

Trignometric relations

sinθ = 1/cscθ

cosθ = 1 /secθ

tanθ = 1/cotθ

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ