Advertisements
Advertisements
प्रश्न
if `cos theta = 3/5`, find the value of `(sin theta - 1/(tan theta))/(2 tan theta)`
Advertisements
उत्तर
We know that `cos theta = "𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒"/"ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒"`
Let us consider right angled Δle ABC
Let x be the opposite side, By applying Pythagoras theorem
𝐴𝐶2 = 𝐴𝐵2 + 𝐵𝐶2
25 = 𝑥2 + 9
𝑥2 = 16 ⇒ 𝑥 = 4
`sin theta = (AB)/(AC) = 4/5`
`tan theta = (AB)/(BC) = 4/3`
Substitute sin 𝜃, tan 𝜃 in the equation we get
`(sin theta 1/(tan theta))/(2 tan theta) = (4/5 - 3/4)/(2 xx 4/3)`
`= ((16 - 15)/20)/(8/3)`
= `(1/20)/(8/3)`
`= 1/20 xx 8/3 = 3/160`
APPEARS IN
संबंधित प्रश्न
In ΔPQR, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`cos A = 4/5`
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`cos theta = 7/25`
If tan θ = `a/b` prove that `(a sin theta - b cos theta)/(a sin theta + b cos theta) = (a^2 - b^2)/(a^2 + b^2)`
If `cos θ = 12/13`, show that `sin θ (1 - tan θ) = 35/156`.
If Cosec A = 2 find `1/(tan A) + (sin A)/(1 + cos A)`
Evaluate the Following
`(sin 30^@ - sin 90^2 + 2 cos 0^@)/(tan 30^@ tan 60^@)`
Evaluate the Following
4(sin4 30° + cos2 60°) − 3(cos2 45° − sin2 90°) − sin2 60°
The value of sin² 30° – cos² 30° is ______.
If cos (40° + A) = sin 30°, then value of A is ______.
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 0° + cos 0° + tan 0° + sec 0°.
Find will be the value of cos 90° + sin 90°.
Find an acute angle θ when `(cos θ - sin θ)/(cos θ + sin θ) = (1 - sqrt(3))/(1 + sqrt(3))`
The maximum value of the expression 5cosα + 12sinα – 8 is equal to ______.
If sinθ = `1/sqrt(2)` and `π/2 < θ < π`. Then the value of `(sinθ + cosθ)/tanθ` is ______.
If cosec θ = `("p" + "q")/("p" - "q")` (p ≠ q ≠ 0), then `|cot(π/4 + θ/2)|` is equal to ______.
If θ is an acute angle and sin θ = cos θ, find the value of tan2 θ + cot2 θ – 2.
Evaluate: 5 cosec2 45° – 3 sin2 90° + 5 cos 0°.
