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Popular >

prove sin(105)=sin(60+45)

Solution

prove

sin (10 5^{\circ}) = sin (6 0^{\circ} + 4 5^{\circ})

Solution

True

Solution steps

sin (10 5^{\circ}) = sin (6 0^{\circ} + 4 5^{\circ})

Manipulating left side

sin (10 5^{\circ})

Expand

sin (10 5^{\circ}) : \frac{3}{2 2} + \frac{1}{2 2}

= \frac{1}{2 2} + \frac{3}{2 2}

Manipulating right side

sin (6 0^{\circ} + 4 5^{\circ})

Rewrite using trig identities

= \frac{6 + 2}{4}

Expand

\frac{2 + 6}{4} : \frac{1}{2 2} + \frac{3}{2 2}

= \frac{1}{2 2} + \frac{3}{2 2}

We showed that the two sides could take the same form

\Rightarrow True

Popular Examples

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prove sin(θ)=-5/12 prove

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prove tan(pi/3)=sqrt(3)prove

tan (\frac{π}{3}) = 3

prove (1+tan^2(x))/(sec(x))=sec(x)prove

\frac{1 + tan ^{2} ( x )}{sec ( x )} = sec (x)

Frequently Asked Questions (FAQ)

Is sin(105)=sin(60+45) ?
The answer to whether sin(105)=sin(60+45) is True