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Prove that: tan10^0tan15^0tan75^0tan80^0...

Prove that: `tan10^0tan15^0tan75^0tan80^0=1` `tan1^0tan2^0tan3^0tan89^0=1` `cos1^0cos2^0cos3^0cos180^0=0`

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`(i)tan10^0tan15^0tan75^0tan80^0`
`=tan(10)^0tan(15)^0tan(75)^0tan(80)^0`
`=tan((90)^0−(80)^0)tan((90)^0−(75)^0)tan(75)^0tan(80)^0`
`=cot(80)^0cot(75)^0tan(75)^0tan(80)^0`
`=(cot(80)^0tan(80)^0)(cot(75)^0tan(75)^0)`
`=1xx1`
`=1`
...
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RD SHARMA-TRIGONOMETRIC RATIOS-All Questions
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  2. Evaluate each of the following: cot 12^0cot 38^0cot52^0cot60^0cot78^0 ...

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  3. Prove that: tan10^0tan15^0tan75^0tan80^0=1 tan1^0tan2^0tan3^0tan89^0=...

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  12. Prove that: (cos30^0+sin60^0)/(1+cos60^0+sin30^0)=(sqrt(3))/2

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  13. Find the value of theta in each of the following: (i)2sin2theta=sqrt...

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  17. If s e c4A=cos e c(A-20^@) , where 4A is an acute angle, find the ...

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  19. Evaluate : 4(sin^4 30^0+cos^4 60^0)-2/3(sin^2 60^0-cos^2 45^0)+1/2tan...

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