Advertisements
Advertisements
प्रश्न
Four alternative answers for the following question are given. Choose the correct alternative and write its alphabet:
sin θ × cosec θ = ______
विकल्प
1
0
`1/2`
`sqrt2`
Advertisements
उत्तर
sin θ × cosec θ = 1
Explanation:
sin θ × cosec θ
= `sintheta xx 1/sinθ ... [cosec theta = 1/(sintheta)]`
= 1
संबंधित प्रश्न
Prove the following trigonometric identities. `(1 - cos A)/(1 + cos A) = (cot A - cosec A)^2`
Prove the following identities:
`1/(1 - sinA) + 1/(1 + sinA) = 2sec^2A`
`(tan A + tanB )/(cot A + cot B) = tan A tan B`
If `(cosec theta - sin theta )= a^3 and (sec theta - cos theta ) = b^3 , " prove that " a^2 b^2 ( a^2+ b^2 ) =1`
If 3 `cot theta = 4 , "write the value of" ((2 cos theta - sin theta))/(( 4 cos theta - sin theta))`
If `sec theta = x ,"write the value of tan" theta`.
If \[\sin \theta = \frac{1}{3}\] then find the value of 2cot2 θ + 2.
If sin2 θ cos2 θ (1 + tan2 θ) (1 + cot2 θ) = λ, then find the value of λ.
If sin θ − cos θ = 0 then the value of sin4θ + cos4θ
Prove the following identity :
`(secθ - tanθ)^2 = (1 - sinθ)/(1 + sinθ)`
If sinA + cosA = m and secA + cosecA = n , prove that n(m2 - 1) = 2m
Without using trigonometric identity , show that :
`sec70^circ sin20^circ - cos20^circ cosec70^circ = 0`
Prove that: 2(sin6θ + cos6θ) - 3 ( sin4θ + cos4θ) + 1 = 0.
Prove that cot θ. tan (90° - θ) - sec (90° - θ). cosec θ + 1 = 0.
Prove that (cosec A - sin A)( sec A - cos A) sec2 A = tan A.
Prove that: sin6θ + cos6θ = 1 - 3sin2θ cos2θ.
If tan θ + cot θ = 2, then tan2θ + cot2θ = ?
Prove that `(cot A)/(1 - tan A) + (tan A)/(1 - cot A) = 1 + tan A + cot A = sec A . "cosec" A + 1`.
sin(45° + θ) – cos(45° – θ) is equal to ______.
Find the value of sin2θ + cos2θ
Solution:
In Δ ABC, ∠ABC = 90°, ∠C = θ°
AB2 + BC2 = `square` .....(Pythagoras theorem)
Divide both sides by AC2
`"AB"^2/"AC"^2 + "BC"^2/"AC"^2 = "AC"^2/"AC"^2`
∴ `("AB"^2/"AC"^2) + ("BC"^2/"AC"^2) = 1`
But `"AB"/"AC" = square and "BC"/"AC" = square`
∴ `sin^2 theta + cos^2 theta = square`
