Question

Express all trigonometric ratios in terms of sin A

Answer 1

Answer:

Hope it helps!! Mark this answer as brainliest if u found it useful and follow me for quick and accurate answers...

Step-by-step explanation:

cos a =  √1-sin2a

sec a = 1/cosa = 1/ √1-sin2a  

tan a = sina/cosa = sina/ √1-sin2a  

cosec a = 1/sina

cot a = cosa / sina =  √1-sin2a / sina

Answer 2

Answer:

All trigonometric ratios can be expressed in terms of Sin A as

$Cos A = \sqrt{1-Sin^2A}\\\\Sec A =\frac{1} \sqrt{1-Sin^ 2A}}\\Tan A = \frac{Sin A}{\sqrt{1-Sin^ 2A}}\\Cot A ={\frac{\sqrt{1-Sin^ 2A}}{Sin A}}\\Cosec= \frac{1}{SinA}$

Step-by-step explanation:

We have expression as Sin A and we have to calculate all the trigonometric ratios in terms of Sin A which can be done by using other identities of trigonometry which can be done as

We know that

$Cos A=\frac{Base }{Hypotenuse}\\\\and Sin^2A +Cos^2A=1\\Cos A = \sqrt{1-sin^2A}$   ......(1)

Hence we got the first trigonometric equation as above now

$Sec A = \frac{Perpendicular}{Base}}\\\\Sec A =\frac{1} \sqrt{1-Sin^ 2A}}$         ......(2)

then

$Tan A= \frac{Perpendicular}{Base}\\Tan A = \frac{Sin A}{\sqrt{1-Sin^ 2A}}$    ....(3)

and

$Cot A = \frac{Base}{Perpendicular}\\Cot A ={\frac{\sqrt{1-Sin^ 2A}}{SinA}$     .....(4)

finally,

$Cosec A = \frac{Hypotenuse}{Perpendicular}\\CosecA= \frac{1}{SinA}$    ....   (5)

Hence all the six trigonometric ratios can be written as above