Advertisements
Advertisements
प्रश्न
Show that : tan 10° tan 15° tan 75° tan 80° = 1
Advertisements
उत्तर
L.H.S. = tan 10° tan 15° tan 75° tan 80°
= tan(90° – 80°) tan(90° – 75°) tan 75° tan 80°
= cot 80° cot 75° tan 75° tan 80° ...[∵ tan(90° – θ] = cot θ]]
= tan 80° cot 80° × tan 75° cot 75°
= 1 × 1
= 1 = R.H.S. ...(∵ tan A cot A = 1)
संबंधित प्रश्न
if `cos theta = 5/13` where `theta` is an acute angle. Find the value of `sin theta`
If `x/a=y/b = z/c` show that `x^3/a^3 + y^3/b^3 + z^3/c^3 = (3xyz)/(abc)`.
Prove the following identities:
`(secA - tanA)/(secA + tanA) = 1 - 2secAtanA + 2tan^2A`
`tan theta/(1+ tan^2 theta)^2 + cottheta/(1+ cot^2 theta)^2 = sin theta cos theta`
Show that none of the following is an identity:
(i) `cos^2theta + cos theta =1`
The value of sin ( \[{45}^° + \theta) - \cos ( {45}^°- \theta)\] is equal to
Prove the following identity:
`cosA/(1 + sinA) = secA - tanA`
Prove the following identity :
`(1 + tan^2θ)sinθcosθ = tanθ`
Without using trigonometric table , evaluate :
`(sin47^circ/cos43^circ)^2 - 4cos^2 45^circ + (cos43^circ/sin47^circ)^2`
If sinθ – cosθ = 0, then the value of (sin4θ + cos4θ) is ______.
