Question

Write all the trigonometric ratios in the form of CosA.

Answer 1

Step-by-step explanation:

Answer:

All trigonometric ratios in terms of cosA.

i) sinA= \sqrt{1-cos^{2}A}i)sinA=1−cos2A

ii ) tanA = \frac{\sqrt{1-cos^{2}A}}{cosA}ii)tanA=cosA1−cos2A

iii) cot A =\frac{cosA}{\sqrt{1-cos^{2}A}}iii)cotA=1−cos2AcosA

iv) secA = \frac{1}{cosA}iv)secA=cosA1

v) cosecA = \frac{1}{\sqrt{1-cos^{2}A}}v)cosecA=1−cos2A1

Step-by-step explanation:

\begin{gathered}We \: know \: the \\ < /p > < p > Trigonometric\: identity:\\\boxed {sin^{2}A = 1-cos^{2}A}\end{gathered}Weknowthe</p><p>Trigonometricidentity:sin2A=1−cos2A

Now ,

i) sinA= \sqrt{1-cos^{2}A}i)sinA=1−cos2A

\begin{gathered}ii ) tanA = \frac{sinA}{cosA}\\=\frac{\sqrt{1-cos^{2}A}}{cosA}\end{gathered}ii)tanA=cosAsinA=cosA1−cos2A

\begin{gathered} iii) cot A = \frac{1}{tanA}\\=\frac{1}{\frac{\sqrt{1-cos^{2}A}}{cosA}}\\=\frac{cosA}{\sqrt{1-cos^{2}A}}\end{gathered}iii)cotA=tanA1=cosA1−cos2A1=1−cos2AcosA

iv) secA = \frac{1}{cosA}iv)secA=cosA1

\begin{gathered}v) cosecA = \frac{1}{sinA}\\=\frac{1}{\sqrt{1-cos^{2}A}}\end{gathered}v)cosecA=sinA1=1−cos2A1

•••♪

Answer 2

all trigonometric ratios in terms of cosA