Advertisements
Advertisements
Question
State whether the following are true or false. Justify your answer.
sec A = `12/5` for some value of angle A.
Options
True
False
Advertisements
Solution
This statement is True.
Explanation:
sec A = `12/5`
`"Hypotenuse"/"Side adjacent to ∠A" - 12/5`
`("AC")/("AB") = (12/5)`
Let AC be 12k, AB will be 5k, where k is a positive integer.
Applying Pythagoras theorem in ΔABC, we obtain
AC2 = AB2 + BC2
(12k)2 = (5k)2 + BC2
144k2 = 25k2 + BC2
BC2 = 119k2
BC = 10.9k
It can be observed that for given two sides AC = 12k and AB = 5k,
BC should be such that,
AC − AB < BC < AC + AB
12k − 5k < BC < 12k + 5k
7k < BC < 17 k
However, BC = 10.9k
Clearly, such a triangle is possible and hence, such value of sec A is possible.
Hence, the given statement is true.
APPEARS IN
RELATED QUESTIONS
If cot θ =` 7/8` evaluate `((1+sin θ )(1-sin θ))/((1+cos θ)(1-cos θ))`
If 4 tan θ = 3, evaluate `((4sin theta - cos theta + 1)/(4sin theta + cos theta - 1))`
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`cos theta = 12/2`
if `tan theta = 12/13` Find `(2 sin theta cos theta)/(cos^2 theta - sin^2 theta)`
If `tan θ = 20/21` show that `(1 - sin theta + cos theta)/(1 + sin theta + cos theta) = 3/7`
Evaluate the following
sin 45° sin 30° + cos 45° cos 30°
Evaluate the following
`2 sin^2 30^2 - 3 cos^2 45^2 + tan^2 60^@`
Evaluate the following
`sin^2 30° cos^2 45 ° + 4 tan^2 30° + 1/2 sin^2 90° − 2 cos^2 90° + 1/24 cos^2 0°`
Evaluate the Following
cosec3 30° cos 60° tan3 45° sin2 90° sec2 45° cot 30°
Evaluate the Following
(cos 0° + sin 45° + sin 30°)(sin 90° − cos 45° + cos 60°)
If `sqrt2 sin (60° – α) = 1` then α is ______.
If cos A + cos² A = 1, then sin² A + sin4 A is equal to ______.
3 sin² 20° – 2 tan² 45° + 3 sin² 70° is equal to ______.
If cos A = `4/5`, then the value of tan A is ______.
Prove the following:
If tan A = `3/4`, then sinA cosA = `12/25`
Find the value of sin 0° + cos 0° + tan 0° + sec 0°.
In the given figure, if sin θ = `7/13`, which angle will be θ?
`sqrt(3)` cos2A + `sqrt(3)` sin2A is equal to ______.
Prove that `tan θ/(1 - cot θ) + cot θ/(1 - tanθ)` = 1 + sec θ cosec θ
If θ is an acute angle and sin θ = cos θ, find the value of tan2 θ + cot2 θ – 2.
