What is the value of cos(arcsin(3/5)-arccos(1/2)) ?

The value of cos(arcsin(3/5)-arccos(1/2)) is 2/5+(3sqrt(3))/(10)

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cos(arcsin(3/5)-arccos(1/2))

cos (arcsin (\frac{3}{5}) - arccos (\frac{1}{2}))

\frac{2}{5} + \frac{3 3}{10}

Decimal Notation

0.91961 \dots

Solution steps

cos (arcsin (\frac{3}{5}) - arccos (\frac{1}{2}))

Rewrite using trig identities:

cos (arcsin (\frac{3}{5})) cos (arccos (\frac{1}{2})) + sin (arcsin (\frac{3}{5})) sin (arccos (\frac{1}{2}))

cos (arcsin (\frac{3}{5}) - arccos (\frac{1}{2}))

Use the Angle Difference identity:

cos (s - t) = cos (s) cos (t) + sin (s) sin (t)

= cos (arcsin (\frac{3}{5})) cos (arccos (\frac{1}{2})) + sin (arcsin (\frac{3}{5})) sin (arccos (\frac{1}{2}))

= cos (arcsin (\frac{3}{5})) cos (arccos (\frac{1}{2})) + sin (arcsin (\frac{3}{5})) sin (arccos (\frac{1}{2}))

Rewrite using trig identities:

cos (arcsin (\frac{3}{5})) = \frac{4}{5}

cos (arcsin (\frac{3}{5}))

Rewrite using trig identities:

cos (arcsin (\frac{3}{5})) = 1 - (\frac{3}{5})^{2}

Use the following identity:

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

= 1 - (\frac{3}{5})^{2}

= 1 - (\frac{3}{5})^{2}

Simplify

= \frac{4}{5}

Rewrite using trig identities:

cos (arccos (\frac{1}{2})) = \frac{1}{2}

Use the following identity:

cos (arccos (x)) = x

= \frac{1}{2}

Rewrite using trig identities:

sin (arcsin (\frac{3}{5})) = \frac{3}{5}

Use the following identity:

sin (arcsin (x)) = x

= \frac{3}{5}

Rewrite using trig identities:

sin (arccos (\frac{1}{2})) = \frac{3}{2}

sin (arccos (\frac{1}{2}))

Rewrite using trig identities:

sin (arccos (\frac{1}{2})) = 1 - (\frac{1}{2})^{2}

Use the following identity:

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

= 1 - (\frac{1}{2})^{2}

= 1 - (\frac{1}{2})^{2}

Simplify

= \frac{3}{2}

= \frac{4}{5} \cdot \frac{1}{2} + \frac{3}{5} \cdot \frac{3}{2}

Simplify

\frac{4}{5} \cdot \frac{1}{2} + \frac{3}{5} \cdot \frac{3}{2} : \frac{2}{5} + \frac{3 3}{10}

\frac{4}{5} \cdot \frac{1}{2} + \frac{3}{5} \cdot \frac{3}{2}

\frac{4}{5} \cdot \frac{1}{2} = \frac{2}{5}

\frac{4}{5} \cdot \frac{1}{2}

Cross-cancel common factor:

2

= \frac{2}{5}

\frac{3}{5} \cdot \frac{3}{2} = \frac{3 3}{10}

\frac{3}{5} \cdot \frac{3}{2}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{3 3}{5 \cdot 2}

Multiply the numbers:

5 \cdot 2 = 10

= \frac{3 3}{10}

= \frac{2}{5} + \frac{3 3}{10}

= \frac{2}{5} + \frac{3 3}{10}

sec (\frac{11 π}{2})

arctan (\frac{9}{10})

arctan (\frac{2.9}{2.8})

sin (\frac{4 π}{11})

tan (1.58)

What is the value of cos(arcsin(3/5)-arccos(1/2)) ?
The value of cos(arcsin(3/5)-arccos(1/2)) is 2/5+(3sqrt(3))/(10)