Question

tan power 2 - sin power 2​

Answer 1

Step-by-step explanation:

tan^2-sin^2=a very tough

Answer 2

Answer:

tan2(θ)−sin2(θ)tan2(θ)-sin2(θ)

Step-by-step explanation:

Rewrite tan(θ)tan(θ) in terms of sines and cosines.

(sin(θ)cos(θ))2−sin2(θ)(sin(θ)cos(θ))2-sin2(θ)

Apply the product rule to sin(θ)cos(θ)sin(θ)cos(θ).

sin2(θ)cos2(θ)−sin2(θ)sin2(θ)cos2(θ)-sin2(θ)

Rewrite sin2(θ)cos2(θ)sin2(θ)cos2(θ) as (sin(θ)cos(θ))2(sin(θ)cos(θ))2.

(sin(θ)cos(θ))2−sin2(θ)

tan2(θ)−sin2(θ)tan2(θ)-sin2(θ)

Simplify each term.

Rewrite tan(θ)tan(θ) in terms of sines and cosines.

(sin(θ)cos(θ))2−sin2(θ)(sin(θ)cos(θ))2-sin2(θ)

Apply the product rule to sin(θ)cos(θ)sin(θ)cos(θ).

sin2(θ)cos2(θ)−sin2(θ)sin2(θ)cos2(θ)-sin2(θ)

Rewrite sin2(θ)cos2(θ)sin2(θ)cos2(θ) as (sin(θ)cos(θ))2(sin(θ)cos(θ))2.

(sin(θ)cos(θ))2−sin2(θ)(sin(θ)cos(θ))2-sin2(θ)

Since both terms are perfect squares, factor using the difference of squares formula, a2−b2=(a+b)(a−b)a2-b2=(a+b)(a-b) where a=sin(θ)cos(θ)a=sin(θ)cos(θ) and b=sin(θ)b=sin(θ).

(sin(θ)cos(θ)+sin(θ))(sin(θ)cos(θ)−sin(θ))(sin(θ)cos(θ)+sin(θ))(sin(θ)cos(θ)-sin(θ))

Convert from sin(θ)cos(θ)sin(θ)cos(θ) to tan(θ)tan(θ).

(tan(θ)+sin(θ))(sin(

Expand (tan(θ)+sin(θ))(tan(θ)−sin(θ))(tan(θ)+sin(θ))(tan(θ)-sin(θ)) using the FOIL Method.

Apply the distributive property.

tan(θ)(tan(θ)−sin(θ))+sin(θ)(tan(θ)−sin(θ))tan(θ)(tan(θ)-sin(θ))+sin(θ)(tan(θ)-sin(θ))

Apply the distributive property.

tan(θ)tan(θ)+tan(θ)(−sin(θ))+sin(θ)(tan(θ)−sin(θ))tan(θ)tan(θ)+tan(θ)(-sin(θ))+sin(θ)(tan(θ)-sin(θ))

Apply the distributive property.

tan(θ)tan(θ)+tan(θ)(−sin(θ))+sin(θ)tan(θ)+sin(θ)(−sin(θ))

tan2(θ)−sin2(θ)tan2(θ)-sin2(θ)

Simplify each term.

Rewrite tan(θ)tan(θ) in terms of sines and cosines.

(sin(θ)cos(θ))2−sin2(θ)(sin(θ)cos(θ))2-sin2(θ)

Apply the product rule to sin(θ)cos(θ)sin(θ)cos(θ).

sin2(θ)cos2(θ)−sin2(θ)sin2(θ)cos2(θ)-sin2(θ)

Rewrite sin2(θ)cos2(θ)sin2(θ)cos2(θ) as (sin(θ)cos(θ))2(sin(θ)cos(θ))2.

(sin(θ)cos(θ))2−sin2(θ)(sin(θ)cos(θ))2-sin2(θ)

Since both terms are perfect squares, factor using the difference of squares formula, a2−b2=(a+b)(a−b)a2-b2=(a+b)(a-b) where a=sin(θ)cos(θ)a=sin(θ)cos(θ) and b=sin(θ)b=sin(θ).

(sin(θ)cos(θ)+sin(θ))(sin(θ)cos(θ)−sin(θ))(sin(θ)cos(θ)+sin(θ))(sin(θ)cos(θ)-sin(θ))

Convert from sin(θ)cos(θ)sin(θ)cos(θ) to tan(θ)tan(θ).

(tan(θ)+sin(θ))(sin(θ)

I can't be bothered to write anymore sorry. I hope it's enough! :D