Question

turn Cos A into Cot A​

Answer 1

Step-by-step explanation:

as we know

$\cos(a ) = \sqrt{1 - { \sin}^{2} a} \\ = \sqrt{1 - { \frac{1}{ \csc ^{2}a } }^{} } \\ = \sqrt{1 - \frac{1}{1 + { \cot \: }^{2} \: a } }$

$a nd \: \: on \: taking \: lcm \: \\ we \: have \: \\ \cos(a) = \\ \sqrt{ \frac{ (cos {}^{2} (a) + 1) - (1)}{ { \cot }^{2} a + 1} } \\ = \sqrt{\frac{{ { \cot}^{2}a } }{ \cot {}^{2} a + 1 } }$

and for more clearity it is more in pic

and I have also expressed cot a in terms of cos a in second pic