Advertisements
Advertisements
प्रश्न
Choose the correct alternative:
cos 45° = ?
पर्याय
sin 45°
sec 45°
cot 45°
tan 45°
उत्तर
sin 45°
cos 45° = `1/sqrt2`, sin 45° = `1/sqrt2`
∴ cos 45° = sin 45°.
APPEARS IN
संबंधित प्रश्न
Prove the identity (sin θ + cos θ)(tan θ + cot θ) = sec θ + cosec θ.
Evaluate without using trigonometric tables:
`cos^2 26^@ + cos 64^@ sin 26^@ + (tan 36^@)/(cot 54^@)`
Prove the following trigonometric identities.
`1/(1 + sin A) + 1/(1 - sin A) = 2sec^2 A`
Prove the following trigonometric identities.
sec6θ = tan6θ + 3 tan2θ sec2θ + 1
Prove that:
`tanA/(1 - cotA) + cotA/(1 - tanA) = secA cosecA + 1`
Show that : `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec A cosec A`
Show that : `sinAcosA - (sinAcos(90^circ - A)cosA)/sec(90^circ - A) - (cosAsin(90^circ - A)sinA)/(cosec(90^circ - A)) = 0`
If `(cot theta ) = m and ( sec theta - cos theta) = n " prove that " (m^2 n)(2/3) - (mn^2)(2/3)=1`
Prove the following identity :
`sec^2A.cosec^2A = tan^2A + cot^2A + 2`
Prove the following identity :
`((1 + tan^2A)cotA)/(cosec^2A) = tanA`
If tanA + sinA = m and tanA - sinA = n , prove that (`m^2 - n^2)^2` = 16mn
Without using trigonometric table , evaluate :
`(sin47^circ/cos43^circ)^2 - 4cos^2 45^circ + (cos43^circ/sin47^circ)^2`
Without using trigonometric identity , show that :
`sin42^circ sec48^circ + cos42^circ cosec48^circ = 2`
If sec θ = `25/7`, then find the value of tan θ.
A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/min.
Prove that `(sin (90° - θ))/cos θ + (tan (90° - θ))/cot θ + (cosec (90° - θ))/sec θ = 3`.
If A + B = 90°, show that sec2 A + sec2 B = sec2 A. sec2 B.
Prove that:
`(cos^3 θ + sin^3 θ)/(cos θ + sin θ) + (cos^3 θ - sin^3 θ)/(cos θ - sin θ) = 2`
Prove that (1 – cos2A) . sec2B + tan2B(1 – sin2A) = sin2A + tan2B
If cos (α + β) = 0, then sin (α – β) can be reduced to ______.