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प्रश्न
Prove that:
`(sinA - cosA)(1 + tanA + cotA) = secA/(cosec^2A) - (cosecA)/(sec^2A)`
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उत्तर
`(sinA - cosA)(1 + tanA + cotA)`
= `sinA + (sin^2A)/cosA + cosA - cosA - sinA - (cos^2A)/sinA`
= `(sin^2A)/cosA - (cos^2A)/sinA`
= `secA/(cosec^2A) - (cosecA)/(sec^2A)`
संबंधित प्रश्न
(1 + tan θ + sec θ) (1 + cot θ − cosec θ) = ______.
Prove the following trigonometric identities.
`tan θ/(1 - cot θ) + cot θ/(1 - tan θ) = 1 + tan θ + cot θ`
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = cosec A - cot A`
`cos^2 theta + 1/((1+ cot^2 theta )) =1`
`1 + (tan^2 θ)/((1 + sec θ)) = sec θ`
If `( cosec theta + cot theta ) =m and ( cosec theta - cot theta ) = n, ` show that mn = 1.
Write True' or False' and justify your answer the following :
The value of \[\cos^2 23 - \sin^2 67\] is positive .
Without using trigonometric identity , show that :
`cos^2 25^circ + cos^2 65^circ = 1`
If `tan θ = 7/24`, then to find value of cos θ complete the activity given below.
Activity:
sec2θ = 1 + `square` ...[Fundamental tri. identity]
sec2θ = 1 + `square^2`
sec2θ = 1 + `square/576`
sec2θ = `square/576`
sec θ = `square`
cos θ = `square` ...`[cos theta = 1/sectheta]`
Simplify (1 + tan2θ)(1 – sinθ)(1 + sinθ)
