What is the value of cos(arctan(sqrt(3))-arcsin((sqrt(3))/2)) ?

The value of cos(arctan(sqrt(3))-arcsin((sqrt(3))/2)) is 1

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cos(arctan(sqrt(3))-arcsin((sqrt(3))/2))

cos (arctan (3) - arcsin (\frac{3}{2}))

1

Solution steps

cos (arctan (3) - arcsin (\frac{3}{2}))

Rewrite using trig identities:

cos (arctan (3)) cos (arcsin (\frac{3}{2})) + sin (arctan (3)) sin (arcsin (\frac{3}{2}))

= cos (arctan (3)) cos (arcsin (\frac{3}{2})) + sin (arctan (3)) sin (arcsin (\frac{3}{2}))

Rewrite using trig identities:

cos (arctan (3)) = \frac{1}{2}

Rewrite using trig identities:

cos (arcsin (\frac{3}{2})) = \frac{1}{2}

Rewrite using trig identities:

sin (arctan (3)) = \frac{3}{2}

Rewrite using trig identities:

sin (arcsin (\frac{3}{2})) = \frac{3}{2}

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

Simplify

\frac{1}{2} \cdot \frac{1}{2} + \frac{3}{2} \cdot \frac{3}{2} : 1

= 1

sin (2) (35)

3 \cdot cos (6 0^{\circ})

arccos (\frac{8.5}{9.9})

csc (\frac{π}{2}) + cot (\frac{π}{2})

sin (\frac{5 π}{9})

What is the value of cos(arctan(sqrt(3))-arcsin((sqrt(3))/2)) ?
The value of cos(arctan(sqrt(3))-arcsin((sqrt(3))/2)) is 1