Advertisements
Advertisements
Question
`(1 + tan^2 "A")/(1 + cot^2 "A")` is equal to ______.
Options
sec2 A
- 1
cot2 A
tan2 A
Advertisements
Solution
`(1 + tan^2 "A")/(1 + cot^2 "A")` is equal to tan2 A.
Explanation:
`(1 + tan^2 "A")/(1 + cot^2 "A") = (1 + (sin^2 "A")/(cos^2 "A"))/(1 + (cos^2 "A")/(sin^2 "A")`
= `((cos^2 "A" + sin^2 "A")/(cos^2 "A"))/((sin^2 "A" + cos^2 "A")/(sin^2 "A")) = (1/cos^2 "A")/(1/sin^2 "A")`
= `sin^2 "A"/cos^2 "A" = tan^2 "A"`
∴ `(1 + tan^2 "A")/(1 + cot^2 "A") = tan^2 "A"`
RELATED QUESTIONS
State whether the following are true or false. Justify your answer.
The value of tan A is always less than 1.
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`tan alpha = 5/12`
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`sec theta = 13/5`
if `tan theta = 12/13` Find `(2 sin theta cos theta)/(cos^2 theta - sin^2 theta)`
Evaluate the following:
(cosec2 45° sec2 30°)(sin2 30° + 4 cot2 45° − sec2 60°)
Evaluate the Following
`4/(cot^2 30^@) + 1/(sin^2 60^@) - cos^2 45^@`
Evaluate the Following
4(sin4 30° + cos2 60°) − 3(cos2 45° − sin2 90°) − sin2 60°
Find the value of x in the following :
`sqrt3 tan 2x = cos 60^@ + sin45^@ cos 45^@`
If 4 tanθ = 3, then `((4 sintheta - costheta)/(4sintheta + costheta))` is equal to ______.
The value of the expression (sin 80° – cos 80°) is negative.
