What is (sin(θ)+cos(θ))^2 ?

The solution to (sin(θ)+cos(θ))^2 is sin(2θ)+1

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simplify (sin(θ)+cos(θ))^2

simplify

(sin (θ) + cos (θ))^{2}

sin (2 θ) + 1

Solution steps

(sin (θ) + cos (θ))^{2}

Expand

(cos (θ) + sin (θ))^{2} : cos^{2} (θ) + 2 cos (θ) sin (θ) + sin^{2} (θ)

= cos^{2} (θ) + sin^{2} (θ) + 2 cos (θ) sin (θ)

Rewrite using trig identities

= sin (2 θ) + 1

(x - 7) (x + 7) - (x - 8) (x + 8)

sin^{2} (x) (1 + cot^{2} (x))

\frac{- 15}{2}

sin (x) (csc (x) - sin (x))

cos^{2} (t) - sin^{2} (t)