If3if 3 cot theta is equals to 4 show that 1 minus 10 squared theta upon 1 + 10 square theta equal to cos square theta minus sin square theta
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Trigonometry Examples
Popular Problems Trigonometry Verify the Identity tan(theta)+cot(theta)=sec(theta)csc(theta)
tan
(
θ
)
+
cot
(
θ
)
=
sec
(
θ
)
csc
(
θ
)
Start on the left side.
tan
(
θ
)
+
cot
(
θ
)
Convert to sines and cosines.
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sin
(
θ
)
cos
(
θ
)
+
cos
(
θ
)
sin
(
θ
)
Add fractions.
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sin
(
θ
)
sin
(
θ
)
+
cos
(
θ
)
cos
(
θ
)
cos
(
θ
)
sin
(
θ
)
Simplify each term.
sin
2
(
θ
)
+
cos
2
(
θ
)
cos
(
θ
)
sin
(
θ
)
Apply pythagorean identity.
1
cos
(
θ
)
sin
(
θ
)
Now consider the right side of the equation.
sec
(
θ
)
csc
(
θ
)
Convert to sines and cosines.
Tap for more steps...
1
cos
(
θ
)
⋅
1
sin
(
θ
)
Multiply
1
cos
(
θ
)
and
1
sin
(
θ
)
.
1
cos
(
θ
)
sin
(
θ
)
Because the two sides have been shown to be equivalent, the equation is an identity.
tan
(
θ
)
+
cot
(
θ
)
=
sec
(
θ
)
csc
(
θ
)
is an identity
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