Advertisements
Advertisements
Question
If sin θ = `12/13`, Find `(sin^2 θ - cos^2 θ)/(2sin θ cos θ) × 1/(tan^2 θ)`.
Solution
Given: Sin θ = `12/13 = "AB"/"AC"`
Let, AB = 12k and AC = 13k
In ΔABC, ∠B = 90°
By pythagoras theorem,
AB2 + BC2 = AC2
(12k)2 + BC2 = (13k)2
144k2 + BC2 = 169k2
BC2 = 169k2 - 144k2
BC2 = 25k2
Taking square root,
BC = 5k
∴ Cos θ = `"BC"/"AC" = "5k"/"13k" = 5/13`
∴ tan θ = `"AB"/"BC" = "12k"/"5k" = 12/5`
Now,
`(sin^2 θ - cos^2 θ)/(2sin θ cos θ) × 1/(tan^2 θ)`.
⇒ `[(12/13)^2 - (5/13)^2]/[2 × 12/13 × 5/13] × 1/(12/5)^2`
⇒ `[(144/169) - (25/169)]/[120/169] × 1/(144/25)`
⇒ `[(144/169) - (25/169)]/[120/169] × 25/144`
⇒ `((144 - 25)/cancel169)/[120/cancel169] × 25/144`
⇒ `119/120 × 25/144`
⇒ `595/3456`
APPEARS IN
RELATED QUESTIONS
Given sec θ = `13/12`, calculate all other trigonometric ratios.
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`cos theta = 7/25`
if `sec A = 17/8` verify that `(3 - 4sin^2A)/(4 cos^2 A - 3) = (3 - tan^2 A)/(1 - 3 tan^2 A)`
If `tan theta = 24/7`, find that sin 𝜃 + cos 𝜃
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
`cot^2 30^@ - 2 cos^2 60^circ- 3/4 sec^2 45^@ - 4 sec^2 30^@`
If cos A = `4/5`, then the value of tan A is ______.
If 4 tanθ = 3, then `((4 sintheta - costheta)/(4sintheta + costheta))` is equal to ______.
Evaluate 2 sec2 θ + 3 cosec2 θ – 2 sin θ cos θ if θ = 45°.
If sin θ – cos θ = 0, then find the value of sin4 θ + cos4 θ.
