Is ((sin(t)+cos(t))^2)/(sin(t)cos(t))=2+sec^2(t)(csc^2(t)) ?

The answer to whether ((sin(t)+cos(t))^2)/(sin(t)cos(t))=2+sec^2(t)(csc^2(t)) is False

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

prove ((sin(t)+cos(t))^2)/(sin(t)cos(t))=2+sec^2(t)(csc^2(t))

prove

\frac{( sin ( t ) + cos ( t ) ) ^{2}}{sin ( t ) cos ( t )} = 2 + sec^{2} (t) (csc^{2} (t))

False

Solution steps

\frac{( sin ( t ) + cos ( t ) ) ^{2}}{sin ( t ) cos ( t )} = 2 + sec^{2} (t) csc^{2} (t)

Show that the two sides are not equal

For

\frac{( sin ( t ) + cos ( t ) ) ^{2}}{sin ( t ) cos ( t )} = 2 + sec^{2} (t) csc^{2} (t)

plug in

t = 1

\frac{( sin ( 1 ) + cos ( 1 ) ) ^{2}}{sin ( 1 ) cos ( 1 )} = 4.19950 \dots

\frac{( sin ( 1 ) + cos ( 1 ) ) ^{2}}{sin ( 1 ) cos ( 1 )}

Refine to a decimal form

= 4.19950 \dots

2 + sec^{2} (1) csc^{2} (1) = 6.83780 \dots

2 + sec^{2} (1) csc^{2} (1)

Refine to a decimal form

= 6.83780 \dots

The two sides are not equal

\Rightarrow False

p ro v e (cot (x) + tan (x)) sin (x) = sec (x)

p ro v e \frac{cos ^{2} ( x )}{1 - sin ( x )} = sin (x) + 1

p ro v e sin^{6} (a) + cos^{6} (a) = 1 - 3 sin^{2} (a) \cdot cos^{2} (a)

p ro v e sin (- 3 x) = - sin (3 x)

p ro v e cos (x) + sin (x) = tan (x) + 1

Is ((sin(t)+cos(t))^2)/(sin(t)cos(t))=2+sec^2(t)(csc^2(t)) ?
The answer to whether ((sin(t)+cos(t))^2)/(sin(t)cos(t))=2+sec^2(t)(csc^2(t)) is False