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प्रश्न
If sin A + cos A = m and sec A + cosec A = n, show that : n (m2 – 1) = 2 m
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उत्तर
Given:
sin A + cos A = m and sec A + cosec A = n
Consider L.H.S = n (m2 – 1)
= `(secA + cosecA)[(sinA + cosA)^2 - 1]`
= `(1/cosA + 1/sinA)[sin^2A + cos^2A + 2sinAcosA - 1]`
= `((cosA + sinA)/(sinAcosA))(1 + 2sinAcosA - 1)`
= `((cosA + sinA))/(sinAcosA)(2sinAcosA)`
= 2(sin A + cos A)
= 2 m = R.H.S
संबंधित प्रश्न
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sec2 A . cosec2 A = tan2 A + cot2 A + 2
If m = a sec A + b tan A and n = a tan A + b sec A, then prove that : m2 – n2 = a2 – b2
If `( cosec theta + cot theta ) =m and ( cosec theta - cot theta ) = n, ` show that mn = 1.
Four alternative answers for the following question are given. Choose the correct alternative and write its alphabet:
sin θ × cosec θ = ______
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sec6 θ = tan6 θ + 3 tan2 θ sec2 θ + 1
Choose the correct alternative:
tan (90 – θ) = ?
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
sec θ when expressed in term of cot θ, is equal to ______.
(1 – cos2 A) is equal to ______.
