Advertisements
Advertisements
प्रश्न
Write True' or False' and justify your answer the following :
The value of the expression \[\sin {80}^° - \cos {80}^°\]
Advertisements
उत्तर
Consider the table.
| θ | 0° | 30° | 45° | 60° | 90° |
| sin θ | 0 | `1/2` | `1/sqrt2` | `sqrt3/2` | 1 |
| cos θ | 1 | `sqrt3/2` | `1/sqrt2` | `1/2` | 0 |
Here,
`sin 60°-cos 60°=sqrt3/2-1/2>0`
`sin 90°-cos 90°= 1-0>0 `
`so, sin 80°-cos 80° > 0` ` (sin θ-cos θ≥0AA45°≤ θ ≤ 90° )`
Therefore, the given statement is false.
APPEARS IN
संबंधित प्रश्न
Express the ratios cos A, tan A and sec A in terms of sin A.
if `cos theta = 5/13` where `theta` is an acute angle. Find the value of `sin theta`
Prove the following identities:
`(1 + sinA)/cosA + cosA/(1 + sinA) = 2secA`
Prove the following identities:
`cosA/(1 - sinA) = sec A + tan A`
Prove the following identities:
(1 + cot A – cosec A)(1 + tan A + sec A) = 2
Prove the following identities:
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
Prove that:
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
`sqrt((1+cos theta)/(1-cos theta)) + sqrt((1-cos theta )/(1+ cos theta )) = 2 cosec theta`
`(sec theta + tan theta )/( sec theta - tan theta ) = ( sec theta + tan theta )^2 = 1+2 tan^2 theta + 25 sec theta tan theta `
Write the value of \[\cot^2 \theta - \frac{1}{\sin^2 \theta}\]
If \[\sin \theta = \frac{4}{5}\] what is the value of cotθ + cosecθ?
Prove the following identity :
`(cot^2θ(secθ - 1))/((1 + sinθ)) = sec^2θ((1-sinθ)/(1 + secθ))`
Prove that: `sqrt((1 - cos θ)/(1 + cos θ)) = "cosec" θ - cot θ`.
Without using the trigonometric table, prove that
cos 1°cos 2°cos 3° ....cos 180° = 0.
Prove that `(sin 70°)/(cos 20°) + (cosec 20°)/(sec 70°) - 2 cos 70° xx cosec 20°` = 0.
Prove that `(cos(90 - "A"))/(sin "A") = (sin(90 - "A"))/(cos "A")`
Prove that `sintheta/(sectheta+ 1) +sintheta/(sectheta - 1)` = 2 cot θ
Prove that `"cot A"/(1 - cot"A") + "tan A"/(1 - tan "A")` = – 1
The value of tan A + sin A = M and tan A - sin A = N.
The value of `("M"^2 - "N"^2) /("MN")^0.5`
Prove the following:
`sintheta/(1 + cos theta) + (1 + cos theta)/sintheta` = 2cosecθ
