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Prove that tan 70^(@)=cot70^(@)+2cot40^(...

Prove that `tan 70^(@)=cot70^(@)+2cot40^(@)`

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To prove that \( \tan 70^\circ = \cot 70^\circ + 2 \cot 40^\circ \), we will start from the left-hand side (LHS) and manipulate it to match the right-hand side (RHS). ### Step-by-Step Solution: 1. **Start with the LHS:** \[ \tan 70^\circ \] ...
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ALLEN-BASIC MATHS LOGARITHIM TRIGNOMETRIC RATIO AND IDENTITIES AND TRIGNOMETRIC EQUATION -ILLUSTRATIONS
  1. Solve for x: (1.25)^(1-x) gt (0.64)^(2(1+sqrt(x))

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  2. Show that log(4)18 is an irrational number.

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  3. If in a right angled triangle, a and b are the lengths of sides and c ...

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  4. If the arcs of same length in two circles subtend angles of 60^(@) and...

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  5. If sintheta+sin^(2)theta=1, then prove that cos^(12)theta+3cos^(10)the...

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  6. 4(sin^(6)theta+cos^(6)theta)-6(sin^(4)theta+cos^(4)theta)is equal to

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  7. If sintheta=-1/2 and tantheta=1/sqrt(3) then theta is equal to,

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  8. Prove that sqrt(3) " cosec "20^(@)-sec 20^(@)=4

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  9. Prove that tan 70^(@)=cot70^(@)+2cot40^(@)

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  10. If sin 2A=lambda sin 2B, prove that : (tan (A+B))/(tan(A-B)) = (lambda...

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  11. (sin5theta+sin2theta-sin tehta)/(cos5theta+2cos3theta+2cos^(2)theta+co...

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  12. Prove that: s in 12^0s in 48^0s in 54^0=1/8dot

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  13. Prove that (2cos2A+1)/(2cos2A-1)=tan(60^0+A)tan(60^0-A)dot

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  14. Prove that: tanA + tan(60^(@)+A) + tan(120^(@)+A)=3tan3A

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  15. sin(671/2)^(@) + cos(671/2)^(@) is equal to A) 1/2sqrt(4+2sqrt(2)), ...

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  16. The value of sin 78^@ - sin 66^@ - sin 42^@ + sin 6^@ is

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  17. In a tringle ABC, sin A-cosB=cosC, then angle B, is

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  18. If A+B+C =(3pi)/(2), then cos2A+cos2B+cos2C is equal to-

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  19. Prove that 5costheta+3cos(theta+pi/3)+3 lies between -4a n d10.

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  20. Find the maximum value of 1+sin(pi/4+theta) + 2cos(pi/4-theta).

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