Question

cot tita = 3/4,tita is acute then cos tita = ?​

Answer 1

ANSWER:

THE VALUE OF COS THETA = 3/5

GIVEN:

$\implies \: cot \theta = \frac{3}{4}$

TO FIND:

$cos \theta$

SOLUTION:

Formulas

$\implies \: 1 + cot {}^{2} \theta = cosec {}^{2} \theta \\ \implies \: sin {}^{2} \theta + cos {}^{2} \theta =1 .........(i)$

By using this formula we can find in the following way:

$\implies \: 1 + (\frac{3}{4}) {}^{2} = cosec {}^{2} \theta \\ \implies \: 1 + \frac{9}{16} = cosec {}^{2} \theta \\ \implies \: \frac{16 + 9}{16} = cosec {}^{2} \theta \\ \implies \: \frac{25}{16} = cosec {}^{2} \theta \\ \implies \: cosec \theta = \sqrt{ \frac{25}{16} } \\ \implies \: cosec \theta = \frac{5}{4} \\ \implies \: sin \theta = \frac{1}{cosec \theta} \\ \implies \: sin \theta = \frac{4}{5} \\ \\ using \: ......(i) \\ \implies \:( \frac{4}{5} ) {}^{2} + cos {}^{2} \theta \: = 1 \\ \implies \: cos {}^{2} \theta = 1 - \frac{16}{25} \\ \implies \: cos \theta \: = \sqrt{ \frac{9}{25} } \\ \implies \: cos \theta \: = \frac{3}{5}$

THE VALUE OF COS THETA = 3/5.

NOTE:

• WE HAVE TO FIRST LEARN THE TRIGONOMETRIC IDENTITIES:
• $\implies \: 1 + cot {}^{2} \theta = cosec {}^{2} \theta \\ \implies \: sin {}^{2} \theta + cos {}^{2} \theta =1 \: \\ \implies \: 1 + tan {}^{2} \theta \: = \: cot {}^{2} \theta$