Advertisements
Advertisements
Question
The value of the expression (cos2 23° – sin2 67°) is positive.
Options
True
False
Solution
This statement is False.
Explanation:
Since, (a2 – b2) = (a + b)(a – b)
cos2 23° – sin2 67° = (cos 23° + sin 67°)(cos 23° – sin 67°)
= [cos 23° + sin(90° – 23°)] [cos 23° – sin(90° – 23°)]
= (cos 23° + cos 23°)(cos 23° – cos 23°) ...(∵ sin(90° – θ) = cos θ)
= (cos 23° + cos 23°).0
= 0, which is neither positive nor negative
APPEARS IN
RELATED QUESTIONS
If sin θ =3/5, where θ is an acute angle, find the value of cos θ.
if `sin theta = 1/sqrt2` find all other trigonometric ratios of angle θ.
if `tan theta = 3/4`, find the value of `(1 - cos theta)/(1 +cos theta)`
if `cot theta = 1/sqrt3` find the value of `(1 - cos^2 theta)/(2 - sin^2 theta)`
Express the following in terms of angle between 0° and 45°:
sin 59° + tan 63°
Use tables to find cosine of 9° 23’ + 15° 54’
Use trigonometrical tables to find tangent of 42° 18'
Evaluate:
`(5sin66^@)/(cos24^@) - (2cot85^@)/(tan5^@)`
Prove that:
tan (55° - A) - cot (35° + A)
∠ACD is an exterior angle of Δ ABC. If ∠B = 40o, ∠A = 70o find ∠ACD.
If \[\cos \theta = \frac{2}{3}\] find the value of \[\frac{\sec \theta - 1}{\sec \theta + 1}\]
If 3 cot θ = 4, find the value of \[\frac{4 \cos \theta - \sin \theta}{2 \cos \theta + \sin \theta}\]
In the following figure the value of cos ϕ is
Prove that `"tan A"/"cot A" = (sec^2"A")/("cosec"^2"A")`
If sin θ + sin² θ = 1 then cos² θ + cos4 θ is equal ______.
2(sin6 θ + cos6 θ) – 3(sin4 θ + cos4 θ) is equal to ______.
If x tan 45° sin 30° = cos 30° tan 30°, then x is equal to ______.
If x tan 60° cos 60°= sin 60° cot 60°, then x = ______.
