हिंदी

Write True' Or False' and Justify Your Answer the Following : the Value of Cos 2 23 − Sin 2 67 is Positive . - Mathematics

Advertisements
Advertisements

प्रश्न

 Write True' or False' and justify your answer  the following : 

The value of  \[\cos^2 23 - \sin^2 67\]  is positive . 

सत्य या असत्य

उत्तर

\[\cos^2 23°- \sin^2 67°\]
\[ = \sin^2 \left( 90°- 23°\right) - \sin^2 67°\]
\[ = \sin^2 67° - \sin^2 67°\]
\[ = 0\] 

Which is not positive, the given statement is false.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 11: Trigonometric Identities - Exercise 11.3 [पृष्ठ ५६]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 10
अध्याय 11 Trigonometric Identities
Exercise 11.3 | Q 24.3 | पृष्ठ ५६

संबंधित प्रश्न

Prove the following trigonometric identities.

`cos theta/(1 + sin theta) = (1 - sin theta)/cos theta`


Prove the following trigonometric identities.

`((1 + tan^2 theta)cot theta)/(cosec^2 theta)   = tan theta`


Prove the following trigonometric identities.

`(1/(sec^2 theta - cos theta) + 1/(cosec^2 theta - sin^2 theta)) sin^2 theta cos^2 theta = (1 - sin^2 theta cos^2 theta)/(2 + sin^2 theta + cos^2 theta)`


Prove the following identities:

`(1 + sinA)/cosA + cosA/(1 + sinA) = 2secA`


Prove the following identities:

`sqrt((1 - sinA)/(1 + sinA)) = cosA/(1 + sinA)`


Prove that:

`(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB) = 0`


`sin theta (1+ tan theta) + cos theta (1+ cot theta) = ( sectheta+ cosec  theta)`


`sin^2 theta + cos^4 theta = cos^2 theta + sin^4 theta`


`(1-tan^2 theta)/(cot^2-1) = tan^2 theta`


` (sin theta + cos theta )/(sin theta - cos theta ) + ( sin theta - cos theta )/( sin theta + cos theta) = 2/ ((1- 2 cos^2 theta))`


If x= a sec `theta + b tan theta and y = a tan theta + b sec theta ,"prove that" (x^2 - y^2 )=(a^2 -b^2)`


Find the value of ` ( sin 50°)/(cos 40°)+ (cosec 40°)/(sec 50°) - 4 cos 50°   cosec 40 °`


Prove the following identity : 

`(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB) = 0`


Prove the following identity : 

`1/(cosA + sinA - 1) + 2/(cosA + sinA + 1) = cosecA + secA`


Without using trigonometric table , evaluate : 

`(sin49^circ/sin41^circ)^2 + (cos41^circ/sin49^circ)^2`


Prove that sec θ. cosec (90° - θ) - tan θ. cot( 90° - θ ) = 1.


Prove that sin( 90° - θ ) sin θ cot θ = cos2θ.


Prove that `tan^3 θ/( 1 + tan^2 θ) + cot^3 θ/(1 + cot^2 θ) = sec θ. cosec θ - 2 sin θ cos θ.`


Prove the following identities.

`sqrt((1 + sin theta)/(1 - sin theta)) + sqrt((1 - sin theta)/(1 + sin theta))` = 2 sec θ


Prove the following:

(sin α + cos α)(tan α + cot α) = sec α + cosec α


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×