What is the value of sin(15)cos(75)+cos(15)sin(75) ?

The value of sin(15)cos(75)+cos(15)sin(75) is 1

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sin(15)cos(75)+cos(15)sin(75)

sin (1 5^{\circ}) cos (7 5^{\circ}) + cos (1 5^{\circ}) sin (7 5^{\circ})

1

Solution steps

sin (1 5^{\circ}) cos (7 5^{\circ}) + cos (1 5^{\circ}) sin (7 5^{\circ})

Rewrite as

= sin (7 5^{\circ}) cos (1 5^{\circ}) + cos (7 5^{\circ}) sin (1 5^{\circ})

Rewrite using trig identities:

sin (9 0^{\circ})

= sin (9 0^{\circ})

Use the following trivial identity:

sin (9 0^{\circ}) = 1

= 1

csc (75 0^{\circ})

cos (111 0^{\circ})

sin (2 arctan (4))

sec (- \frac{7 π}{2})

\frac{10}{sin ( 4 5 ^{\circ} )}

What is the value of sin(15)cos(75)+cos(15)sin(75) ?
The value of sin(15)cos(75)+cos(15)sin(75) is 1