Advertisements
Advertisements
प्रश्न
Prove that sec θ + tan θ = `cos θ/(1 - sin θ)`.
Proof: L.H.S. = sec θ + tan θ
= `1/square + square/square`
= `square/square` ......`(∵ sec θ = 1/square, tan θ = square/square)`
= `((1 + sin θ) square)/(cos θ square)` ......[Multiplying `square` with the numerator and denominator]
= `(1^2 - square)/(cos θ square)`
= `square/(cos θ square)`
= `cos θ/(1 - sin θ)` = R.H.S.
∴ L.H.S. = R.H.S.
∴ sec θ + tan θ = `cos θ/(1 - sin θ)`
Advertisements
उत्तर
Proof: L.H.S. = sec θ + tan θ
= `1/bb(cos θ) + bb(sin θ)/bb(cos θ)` ........`[∵ sec θ = 1/bb(cos θ), tan θ = bb(sin θ)/bb(cos θ)]`
= `bb(1 + sintheta)/bbcostheta` = `((1 + sin θ) bb(1 - sin θ))/(cos θ bb(1 - sin θ)` ......[Multiplying `bb(1 - sin θ)` with the numerator and denominator]
= `(1^2 - bb(sin^2 θ))/(cos θ bb(1 - sin θ)`
= `bb (cos^2 θ)/(cos θ bb(1 - sin θ)`
= `cos θ/(1 - sin θ)` = R.H.S.
∴ L.H.S. = R.H.S.
∴ sec θ + tan θ = `cos θ/(1 - sin θ)`
APPEARS IN
संबंधित प्रश्न
In ΔABC right angled at B, AB = 24 cm, BC = 7 m. Determine:
sin C, cos C
State whether the following are true or false. Justify your answer.
sec A = `12/5` for some value of angle A.
State whether the following are true or false. Justify your answer.
cos A is the abbreviation used for the cosecant of angle A.
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`sin A = 2/3`
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`sec theta = 13/5`
If 3 tan θ = 4, find the value of `(4cos theta - sin theta)/(2cos theta + sin theta)`
If `sin theta = a/b` find sec θ + tan θ in terms of a and b.
If `tan θ = 20/21` show that `(1 - sin theta + cos theta)/(1 + sin theta + cos theta) = 3/7`
Evaluate the following
sin 45° sin 30° + cos 45° cos 30°
Evaluate the following
`2 sin^2 30^2 - 3 cos^2 45^2 + tan^2 60^@`
Evaluate the Following
cosec3 30° cos 60° tan3 45° sin2 90° sec2 45° cot 30°
The value of the expression `[(sin^2 22^circ + sin^2 68^circ)/(cos^2 22^circ + cos^2 68^circ) + sin^2 63^circ + cos 63^circ sin 27^circ]` is ______.
In ΔABC, ∠ABC = 90° and ∠ACB = θ. Then write the ratios of sin θ and tan θ from the figure.
Find the value of sin 45° + cos 45° + tan 45°.
What will be the value of sin 45° + `1/sqrt(2)`?
Prove that: cot θ + tan θ = cosec θ·sec θ
Proof: L.H.S. = cot θ + tan θ
= `square/square + square/square` ......`[∵ cot θ = square/square, tan θ = square/square]`
= `(square + square)/(square xx square)` .....`[∵ square + square = 1]`
= `1/(square xx square)`
= `1/square xx 1/square`
= cosec θ·sec θ ......`[∵ "cosec" θ = 1/square, sec θ = 1/square]`
= R.H.S.
∴ L.H.S. = R.H.S.
∴ cot θ + tan θ = cosec·sec θ
Let f(x) = sinx.cos3x and g(x) = cosx.sin3x, then the value of `7((f(π/7) + g(π/7))/(g((5π)/14) + f((5π)/14)))` is ______.
