Is csc^2(x)+2cot(x)=(1+cot(x))^2 ?

The answer to whether csc^2(x)+2cot(x)=(1+cot(x))^2 is True

Popular >

prove csc^2(x)+2cot(x)=(1+cot(x))^2

prove

csc^{2} (x) + 2 cot (x) = (1 + cot (x))^{2}

True

Solution steps

csc^{2} (x) + 2 cot (x) = (1 + cot (x))^{2}

Manipulating left side

csc^{2} (x) + 2 cot (x)

Rewrite using trig identities

= 1 + cot^{2} (x) + 2 cot (x)

Manipulating right side

(1 + cot (x))^{2}

Expand

(1 + cot (x))^{2} : 1 + 2 cot (x) + cot^{2} (x)

= 1 + cot^{2} (x) + 2 cot (x)

We showed that the two sides could take the same form

\Rightarrow True

csc (t) cot (t) = \frac{1 + cot ^{2} ( t )}{sec ( t )}

csc (a) sec (a) = 2 csc (2 a)

tan^{2} (\frac{x}{2}) = \frac{sec ( x ) - 1}{sec ( x ) + 1}

tan^{2} (2 x) + 1 = sec^{2} (2 x)

sin (4 θ) = 4 sin (θ) cos (θ) cos (2 θ)

Is csc^2(x)+2cot(x)=(1+cot(x))^2 ?
The answer to whether csc^2(x)+2cot(x)=(1+cot(x))^2 is True