What is (sin(x)+csc(x))^2+(cos(x)+sec(x))^2 ?

The solution to (sin(x)+csc(x))^2+(cos(x)+sec(x))^2 is csc^2(x)+sec^2(x)+5

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simplify (sin(x)+csc(x))^2+(cos(x)+sec(x))^2

simplify

(sin (x) + csc (x))^{2} + (cos (x) + sec (x))^{2}

csc^{2} (x) + sec^{2} (x) + 5

Solution steps

(sin (x) + csc (x))^{2} + (cos (x) + sec (x))^{2}

Expand

(sin (x) + csc (x))^{2} : csc^{2} (x) + sin^{2} (x) + 2

= csc^{2} (x) + sin^{2} (x) + 2 + (cos (x) + sec (x))^{2}

Expand

(cos (x) + sec (x))^{2} : cos^{2} (x) + 2 cos (x) sec (x) + sec^{2} (x)

= csc^{2} (x) + sin^{2} (x) + 2 + cos^{2} (x) + 2 cos (x) sec (x) + sec^{2} (x)

Use the Pythagorean identity:

cos^{2} (x) + sin^{2} (x) = 1

= csc^{2} (x) + sec^{2} (x) + 2 cos (x) sec (x) + 2 + 1

Add the numbers:

2 + 1 = 3

= csc^{2} (x) + sec^{2} (x) + 2 cos (x) sec (x) + 3

sec (x) cos (x) = 1

= csc^{2} (x) + sec^{2} (x) + 3 + 2 \cdot 1

Multiply the numbers:

2 \cdot 1 = 2

= csc^{2} (x) + sec^{2} (x) + 3 + 2

Add the numbers:

3 + 2 = 5

= csc^{2} (x) + sec^{2} (x) + 5

ln (9)

2 lo g_{4} (8) x^{3} y

\frac{x + 7}{( x - 6 ) ( x - 7 )}

(r^{3} \cdot cos (θ) 3 + r^{4} \cdot cos (θ) 4 - r^{2} \cdot cos (θ) 2)^{2}

a (2, - 8, 32) + b (- 4, 18, - 70) + c (- 20, 95, - 370)

What is (sin(x)+csc(x))^2+(cos(x)+sec(x))^2 ?
The solution to (sin(x)+csc(x))^2+(cos(x)+sec(x))^2 is csc^2(x)+sec^2(x)+5