Is cos(15)=cos(45-30) ?

The answer to whether cos(15)=cos(45-30) is True

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prove cos(15)=cos(45-30)

prove

cos (1 5^{\circ}) = cos (4 5^{\circ} - 3 0^{\circ})

True

Solution steps

cos (1 5^{\circ}) = cos (4 5^{\circ} - 3 0^{\circ})

Manipulating left side

cos (1 5^{\circ})

Simplify

cos (1 5^{\circ}) : \frac{6 + 2}{4}

= \frac{2 + 6}{4}

Manipulating right side

cos (4 5^{\circ} - 3 0^{\circ})

Rewrite using trig identities

= \frac{6 + 2}{4}

We showed that the two sides could take the same form

\Rightarrow True

1 - csc^{2} (x) = - cot^{2} (x)

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

sin (θ) cos (θ) csc^{2} (θ) = cot (θ)

\frac{1 + tan ( θ )}{sin ( θ ) + cos ( θ )} = sec (θ)

\frac{cos ( x ) sec ( x )}{cot ( x )} = tan (x)