Advertisements
Advertisements
प्रश्न
(1 + tan θ + sec θ) (1 + cot θ − cosec θ) = ______.
विकल्प
0
1
2
-1
none of these
Advertisements
उत्तर
(1 + tan θ + sec θ) (1 + cot θ − cosec θ) = 2.
Explanation:
(1 + tan θ + sec θ) (1 + cot θ − cosec θ)
= `(1+ (sin theta)/(cos theta)+1/(costheta))(1+(costheta)/(sin theta)-1/(sin theta))`
= `((costheta+sintheta +1)/costheta)((sintheta+cos theta -1)/sintheta)`
= `((sintheta+costheta)^2-(1)^2)/(sinthetacostheta)`
= `(sin^2theta+cos^2 theta + 2sin theta cos theta -1)/(sinthetacostheta)`
= `(1+2sinthetacostheta -1)/(sinthetacostheta)`
= `(2sintheta costheta)/(sin theta costheta)`
= 2
Hence, alternative 2 is correct.
APPEARS IN
संबंधित प्रश्न
Without using trigonometric tables evaluate
`(sin 35^@ cos 55^@ + cos 35^@ sin 55^@)/(cosec^2 10^@ - tan^2 80^@)`
Prove the following trigonometric identities.
`tan theta - cot theta = (2 sin^2 theta - 1)/(sin theta cos theta)`
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:
cosec A(1 + cos A) (cosec A – cot A) = 1
If tan A = n tan B and sin A = m sin B, prove that `cos^2A = (m^2 - 1)/(n^2 - 1)`
If sin2 θ cos2 θ (1 + tan2 θ) (1 + cot2 θ) = λ, then find the value of λ.
If cos \[9\theta\] = sin \[\theta\] and \[9\theta\] < 900 , then the value of tan \[6 \theta\] is
Prove the following identity :
`sec^4A - sec^2A = sin^2A/cos^4A`
Prove that: 2(sin6 θ + cos6 θ) – 3 (sin4 θ + cos4 θ) + 1 = 0.
Prove that `(cos θ)/(1 - sin θ) = (1 + sin θ)/(cos θ)`.
