trigonometry!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Question

Verify tan x +2 cot x =sec x csc x+cot x

Answer 1

LHS tan(x) + 2cot(x)

tan(x) + cot(x) + cot(x)

Quotient Identities: tan(θ) = sin(θ)/cos(θ) and cot(θ) = cos(θ)/sin(θ)

[sin(x)/cos(x) + cos(x)/sin(x)] + cot(x)

Rewrite the expression with common denominator.

[sin²(x) + cos²(x)]/[sin(x)cos(x)] + cot(x)

Pythagorean Identities: sin²(θ) + cos²(θ) = 1

1/[sin(x)cos(x)] + cot(x)

[1/sin(x)]*[1/cos(x)] + cot(x)

Reciprocal identities: 1/isn(θ)=coses(θ) and 1/cos(θ)=sec(θ).

coses(x)sec(x) + cot(x) RHS

Therefore tan(x) + 2cot(x) = sec(x)coses(x) + cot(x).

Answer 2

The trigonometric equation is tan x + 2 cot x = sec x csc x + cot x.

Right hand side identity = sec x csc x + cot x.

Using reciprocal identities : sec x = 1/cos x and csc x = 1/sin x.

sec x csc x + cot x = (1/cos x)(1/sin x) + cot x

= (1/cos x sin x) + cot x

Pythagorean Identities: sin²(x) + cos²(x) = 1.

= (sin²x + cos²x)/(cos x sin x) + cot x

= (sin²x/cos x sin x) + (cos²x/cos x sin x) + cot x

= (sin x/cos x) + (cos x/sin x) + cot x

Trigonometry identities : tan x = sin x/cos x and cot x = cos x/sin x.

= tan x + cot x + cot x

= tan x + 2 cot x

= Left hand side identity.