Advertisements
Advertisements
प्रश्न
Find the value of ` ( sin 50°)/(cos 40°)+ (cosec 40°)/(sec 50°) - 4 cos 50° cosec 40 °`
उत्तर
`(sin 50°)/(cos 40 °)+ ( cosec 40° )/( sec 50°) - 4 cos 50° cosec 40°`
`=(cos (90°- 50°))/(cos 40°) + (sec (90°- 40°))/(sec 50°)- 4 sin (90°-50°) cosec 40°`
`=(cos 40° )/( cos 40 °) + ( sec50°)/( sec 50°) - 4 sin 40 ° xx 1/ ( sin 40 °)`
= 1 + 1 - 4
= - 2
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities:
(i) (1 – sin2θ) sec2θ = 1
(ii) cos2θ (1 + tan2θ) = 1
Prove the following trigonometric identities.
if `T_n = sin^n theta + cos^n theta`, prove that `(T_3 - T_5)/T_1 = (T_5 - T_7)/T_3`
Prove the following identities:
(sin A + cosec A)2 + (cos A + sec A)2 = 7 + tan2 A + cot2 A
Prove the following identities:
(1 + cot A – cosec A)(1 + tan A + sec A) = 2
Prove that:
`(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB) = 0`
Show that : `sinAcosA - (sinAcos(90^circ - A)cosA)/sec(90^circ - A) - (cosAsin(90^circ - A)sinA)/(cosec(90^circ - A)) = 0`
Prove the following identities:
cosec4 A (1 – cos4 A) – 2 cot2 A = 1
`sin^6 theta + cos^6 theta =1 -3 sin^2 theta cos^2 theta`
`sin theta/((cot theta + cosec theta)) - sin theta /( (cot theta - cosec theta)) =2`
`(sin theta+1-cos theta)/(cos theta-1+sin theta) = (1+ sin theta)/(cos theta)`
Write the value of `cosec^2 theta (1+ cos theta ) (1- cos theta).`
If `cos B = 3/5 and (A + B) =- 90° ,`find the value of sin A.
Write the value of tan10° tan 20° tan 70° tan 80° .
Write True' or False' and justify your answer the following :
The value of sin θ+cos θ is always greater than 1 .
Prove the following identity :
secA(1 + sinA)(secA - tanA) = 1
Prove that:
tan (55° + x) = cot (35° – x)
Without using the trigonometric table, prove that
tan 10° tan 15° tan 75° tan 80° = 1
Prove the following identities:
`1/(sin θ + cos θ) + 1/(sin θ - cos θ) = (2sin θ)/(1 - 2 cos^2 θ)`.
Prove the following identities.
`(cot theta - cos theta)/(cot theta + cos theta) = ("cosec" theta - 1)/("cosec" theta + 1)`
If cos (α + β) = 0, then sin (α – β) can be reduced to ______.
