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प्रश्न
Statement 1: sin2θ + cos2θ = 1
Statement 2: cosec2θ + cot2θ = 1
Which of the following is valid?
पर्याय
Only 1
Only 2
Both 1 and 2
Neither 1 nor 2
उत्तर
Only 1
Explanation:
From statement 2: cosec2θ – cot2θ = 1 is correct
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संबंधित प्रश्न
Prove the following identities:
`(i) cos4^4 A – cos^2 A = sin^4 A – sin^2 A`
`(ii) cot^4 A – 1 = cosec^4 A – 2cosec^2 A`
`(iii) sin^6 A + cos^6 A = 1 – 3sin^2 A cos^2 A.`
If` (sec theta + tan theta)= m and ( sec theta - tan theta ) = n ,` show that mn =1
Prove the following identity :
(secA - cosA)(secA + cosA) = `sin^2A + tan^2A`
Prove that sin2 θ + cos4 θ = cos2 θ + sin4 θ.
If A + B = 90°, show that `(sin B + cos A)/sin A = 2tan B + tan A.`
Prove the following identities.
`costheta/(1 + sintheta)` = sec θ – tan θ
Prove that sec2θ − cos2θ = tan2θ + sin2θ
To prove cot θ + tan θ = cosec θ × sec θ, complete the activity given below.
Activity:
L.H.S = `square`
= `square/sintheta + sintheta/costheta`
= `(cos^2theta + sin^2theta)/square`
= `1/(sintheta*costheta)` ......`[cos^2theta + sin^2theta = square]`
= `1/sintheta xx 1/square`
= `square`
= R.H.S
If `sqrt(3) tan θ` = 1, then find the value of sin2θ – cos2θ.
If 2sin2θ – cos2θ = 2, then find the value of θ.
