Advertisements
Advertisements
प्रश्न
Prove that `(sin θ + tan θ)/(cos θ) = tan θ (1 + sec θ)`.
Advertisements
उत्तर
L.H.S. = `(sin θ + tan θ)/(cos θ)`
= `(sin θ)/(cos θ) + (tan θ)/(cos θ)`
= tan θ + tan θ sec θ
= tan θ (1 + sec θ)
= R.H.S.
∴ `(sin θ + tan θ)/(cos θ) = tan θ (1 + sec θ)`
APPEARS IN
संबंधित प्रश्न
Given that:
(1 + cos α) (1 + cos β) (1 + cos γ) = (1 − cos α) (1 − cos α) (1 − cos β) (1 − cos γ)
Show that one of the values of each member of this equality is sin α sin β sin γ
Prove the following identities:
`1/(1 - sinA) + 1/(1 + sinA) = 2sec^2A`
Prove the following identities:
`(sintheta - 2sin^3theta)/(2cos^3theta - costheta) = tantheta`
Prove the following identities:
`(1+ sin A)/(cosec A - cot A) - (1 - sin A)/(cosec A + cot A) = 2(1 + cot A)`
`(sin theta+1-cos theta)/(cos theta-1+sin theta) = (1+ sin theta)/(cos theta)`
Write the value of `sin theta cos ( 90° - theta )+ cos theta sin ( 90° - theta )`.
Find the value of sin ` 48° sec 42° + cos 48° cosec 42°`
If sin θ = `11/61`, find the values of cos θ using trigonometric identity.
What is the value of (1 − cos2 θ) cosec2 θ?
If \[\cos A = \frac{7}{25}\] find the value of tan A + cot A.
Write True' or False' and justify your answer the following :
The value of the expression \[\sin {80}^° - \cos {80}^°\]
Prove the following identity :
`(secA - 1)/(secA + 1) = (1 - cosA)/(1 + cosA)`
Find the value of x , if `cosx = cos60^circ cos30^circ - sin60^circ sin30^circ`
Without using trigonometric identity , show that :
`sin(50^circ + θ) - cos(40^circ - θ) = 0`
Without using trigonometric identity , show that :
`sec70^circ sin20^circ - cos20^circ cosec70^circ = 0`
Prove that `( 1 + sin θ)/(1 - sin θ) = 1 + 2 tan θ/cos θ + 2 tan^2 θ` .
Prove that identity:
`(sec A - 1)/(sec A + 1) = (1 - cos A)/(1 + cos A)`
1 + cot2θ = ?
If `tan θ = 13/12`, then cot θ = ?
If cos 9α = sinα and 9α < 90°, then the value of tan5α is ______.
