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प्रश्न
(1 + sin A)(1 – sin A) is equal to ______.
विकल्प
cosec2A
sin2A
sec2A
cos2A
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उत्तर
(1 + sin A)(1 – sin A) is equal to cos2A.
Explanation:
(1 + sin A)(1 – sin A) = (1)2 – (sin A)2 ......{(a + b)(a – b) = (a2 – b2)}
= 1 – sin2A
= cos2A
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संबंधित प्रश्न
Prove that:
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`(sec theta -1 )/( sec theta +1) = ( sin ^2 theta)/( (1+ cos theta )^2)`
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Prove the following identities:
`(tan"A"+tan"B")/(cot"A"+cot"B")=tan"A"tan"B"`
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Find the value of sin2θ + cos2θ
Solution:
In Δ ABC, ∠ABC = 90°, ∠C = θ°
AB2 + BC2 = `square` .....(Pythagoras theorem)
Divide both sides by AC2
`"AB"^2/"AC"^2 + "BC"^2/"AC"^2 = "AC"^2/"AC"^2`
∴ `("AB"^2/"AC"^2) + ("BC"^2/"AC"^2) = 1`
But `"AB"/"AC" = square and "BC"/"AC" = square`
∴ `sin^2 theta + cos^2 theta = square`
