Tan^2theta - Sin^2theta = tan^2theta. sin^2theta
explain this step
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tan²(θ) - sin²(θ) = sin²(θ)/cos²(θ) - sin²(θ)

-- because tan(θ) = sin(θ)/cos(θ) by definition of tangent --

… = sin²(θ) (1/cos²(θ) - 1)

-- we pull out the common factor of sin²(θ) from both terms --

… = sin²(θ) (1/cos²(θ) - cos²(θ)/cos²(θ))

-- because x/x = 1 (so long as x ≠ 0) --

… = sin²(θ) ((1 - cos²(θ))/cos²(θ))

-- we simply combine the fractions, which we can do because of the common denominator of cos²(θ) --

… = sin²(θ) (sin²(θ)/cos²(θ))

-- due to the Pythagorean identity, sin²(θ) + cos²(θ) = 1 --

… = sin²(θ) tan²(θ)

-- again, by definition of tan(θ) --

ruth is 6 years old

step-by-step explanation:

6 + 24 = 30,   so 6/30 = .2  

if you do 1/5 it also equals .2, so that is the answer.

7.25

step-by-step explanation:

we know that 7 equals to 7.0. we also know that 1/4=0.25. so we can add the two together and we get 7.25