Is sec(β)sin(β)cot(β)=1 ?

The answer to whether sec(β)sin(β)cot(β)=1 is True

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prove sec(β)sin(β)cot(β)=1

prove

sec (β) sin (β) cot (β) = 1

True

Solution steps

sec (β) sin (β) cot (β) = 1

Manipulating left side

sec (β) sin (β) cot (β)

Express with sin, cos

cot (β) sec (β) sin (β)

Use the basic trigonometric identity:

cot (x) = \frac{cos ( x )}{sin ( x )}

= \frac{cos ( β )}{sin ( β )} sec (β) sin (β)

Use the basic trigonometric identity:

sec (x) = \frac{1}{cos ( x )}

= \frac{cos ( β )}{sin ( β )} \cdot \frac{1}{cos ( β )} sin (β)

\frac{cos ( β )}{sin ( β )} \cdot \frac{1}{cos ( β )} sin (β) = 1

\frac{cos ( β )}{sin ( β )} \cdot \frac{1}{cos ( β )} sin (β)

Multiply fractions:

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

= \frac{cos ( β ) \cdot 1 \cdot sin ( β )}{sin ( β ) cos ( β )}

Cancel the common factor:

cos (β)

= \frac{1 \cdot sin ( β )}{sin ( β )}

Cancel the common factor:

sin (β)

= 1

= 1

= 1

We showed that the two sides could take the same form

\Rightarrow True

1 - sin^{2} (θ) + sin^{4} (θ) = cos^{4} (θ)

sec (x) - tan (x) = \frac{cos ^{2} ( x )}{sin ( x )}

3 - 6 sin^{2} (x) = - 3 cos (2 x)

(sin (\frac{5 \cdot \frac{π}{3}}{4})) = (sin (5 \frac{π}{12}))

tan (\frac{5 π}{12}) = tan (\frac{π}{4} + \frac{π}{6})