Advertisements
Advertisements
प्रश्न
Prove that `2 sin^2 (3pi)/4 + 2 cos^2 pi/4 + 2 sec^2 pi/3` = 10
उत्तर
`sin (3pi)/4 = sin 3 xx 45^circ = sin 135^circ`
= sin (180 - 45)
= sin 45° = `1/sqrt2`
`sec ((pi/3)) = 2`
`therefore 2 sin^2 ((3pi)/4) + 2 cos^2 pi/4 + 2 sec^2 pi/3`
`= 2 (sin (3pi)/4)^2 + 2 (cos pi/4)^2 + 2 (sec pi/3)^2`
`= 2 (1/sqrt2)^2 + 2 (1/sqrt2)^2 + 2 (2)^2`
`= cancel(2)(1/cancel(2)) + cancel(2)(1/cancel(2)) + 2 (2)^2`
= 1 + 1 + 8 = 10
Hence proved.
APPEARS IN
संबंधित प्रश्न
Find the value of the following:
sin 76° cos 16° – cos 76° sin 16°
Find the value of the following:
cos 70° cos 10° – sin 70° sin 10°
If cot α = `1/2`, sec β = `(-5)/3`, where π < α < `(3pi)/2 and pi/2` < β < π, find the value of tan(α + β). State the quadrant in which α + β terminates.
If tan θ = 3 find tan 3θ
If sin A = `12/13`, find sin 3A.
If tan x = `3/4` and `pi < x < (3pi)/2`, then find the value of sin `x/2` and cos `x/2`.
The value of sin (-420°)
If sin A + cos A = 1 then sin 2A is equal to:
The value of `(2 tan 30^circ)/(1 + tan^2 30^circ)` is:
If tan A = `1/2` and tan B = `1/3` then tan(2A + B) is equal to:
