What is the value of 5sin^2(40)+5cos^2(40) ?

The value of 5sin^2(40)+5cos^2(40) is 5

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5sin^2(40)+5cos^2(40)

5 sin^{2} (4 0^{\circ}) + 5 cos^{2} (4 0^{\circ})

5

Solution steps

5 sin^{2} (4 0^{\circ}) + 5 cos^{2} (4 0^{\circ})

Rewrite using trig identities:

cos^{2} (4 0^{\circ}) = 1 - sin^{2} (4 0^{\circ})

cos^{2} (4 0^{\circ})

Use the Pythagorean identity:

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

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

= 1 - sin^{2} (4 0^{\circ})

= 5 sin^{2} (4 0^{\circ}) + 5 (1 - sin^{2} (4 0^{\circ}))

Simplify

= 5

cos (31 0^{\circ}) cos (5 0^{\circ}) - sin (31 0^{\circ}) sin (5 0^{\circ})

arctan (\frac{6}{- 6})

cos (\frac{29 π}{12})

arctan (\frac{3}{- 3 3})

tan (arccos (\frac{24}{25}) - arcsin (\frac{12}{13}))

What is the value of 5sin^2(40)+5cos^2(40) ?
The value of 5sin^2(40)+5cos^2(40) is 5