Transformation Formulae - Maharashtra Board STD 11 Maths Questions

$\text{If }\cos(\text{A+B})\sin(\text{C}-\text{D})=\cos(\text{A}-\text{B})\sin(\text{C+D}),$
than write the value $\tan\text{A}\tan\text{B}\tan\text{C}.$

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Q 11Solve the Following Question.(2 Marks)2 Marks

Prove that:
$\sin47^\circ+\cos77^\circ=\cos17^\circ$

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Q 12Solve the Following Question.(2 Marks)2 Marks

Prove that:
$\sin\frac{5\pi}{18}-\cos\frac{4\pi}{9}=\sqrt3\sin\frac{\pi}{9}$

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Q 13Solve the Following Question.(2 Marks)2 Marks

Prove that:
$\sin65^\circ+\cos65^\circ=\sqrt2\cos20^\circ$

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Q 14Solve the Following Question.(2 Marks)2 Marks

Prove that:
$\sin105^\circ+\cos105^\circ=\cos45^\circ$

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Q 15Solve the Following Question.(2 Marks)2 Marks

Prove that:
$\cos80^\circ+\cos40^\circ-\cos20^\circ=0$

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Q 16Solve the Following Question.(3 Marks)3 Marks

Prove that:
$\frac{\sin9\text{A}-\sin\text7{A}}{\cos7\text{A}-\cos9\text{A}}=\cot8\text{A}$

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Q 17Solve the Following Question.(3 Marks)3 Marks

$\text{If}\ \text{cosec}\text{A}+\sec\text{A}=\text{cosecB}+\sec\text{B},$ prove that:
$\tan\text{A}\tan\text{B}=\cot\frac{\text{A+B}}{2}$

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Q 18Solve the Following Question.(3 Marks)3 Marks

Prove that:
$\frac{\sin\text{A}-\sin\text{B}}{\cos\text{A}+\cos\text{B}}=\tan\frac{\text{A}-\text{B}}{2}$

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Q 19Solve the Following Question.(4 Marks)4 Marks

$\text{If}\ \cos(\text{A+B})\sin(\text{C}-\text{D})=\cos(\text{A}-\text{B})\sin(\text{C+D}),$
prove that $\tan\text{A}\tan\text{B}\tan\text{C}+\tan\text{D}=0$

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Q 20Solve the Following Question.(4 Marks)4 Marks

Prove that:
$\sin\text{A}+\sin2\text{A}+\sin4\text{A}+\sin5\text{A}=4\cos\frac{\text{A}}{2}\cos\frac{2\text{A}}{2}\cos4\text{A}$

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Q 21Solve the Following Question.(4 Marks)4 Marks

Prove that:
$\tan20^\circ\tan40^\circ\tan60^\circ\tan80^\circ=3$

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Q 22Solve the Following Question.(4 Marks)4 Marks

Prove that:
$\sin10^\circ\sin50^\circ\sin60^\circ\sin70^\circ=\frac{\sqrt3}{16}$

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Q 23Solve the Following Question.(4 Marks)4 Marks

Prove that:
$\frac{\sin3\text{A}+\sin5\text{A}+\sin7\text{A}+\sin9\text{A}}{\cos3\text{A}+\cos5\text{A}+\cos7\text{A}\cos9\text{A}}=\tan6\text{A}$

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Q 24Solve the Following Question.(5 Marks)5 Marks

Prove that:
$\cos20^\circ\cos100^\circ+\cos100^\circ\cos140^\circ-\cos140^\circ\cos200^\circ=-\frac{3}{4}$

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Q 25Solve the Following Question.(5 Marks)5 Marks

Prove that:
$\cos(\text{A+B+C})+\cos(\text{A}-\text{B+C})+\cos(\text{A+B}-\text{C})\\+\cos(-\text{A+B+C})=4\cos\text{A}\cos\text{B}\cos\text{C}$

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Q 26Solve the Following Question.(5 Marks)5 Marks

prove that:
$\sin(\text{B}-\text{C})\cos(\text{A}-\text{D})+\sin(\text{C}-\text{A})\cos(\text{B}-\text{D})+\sin(\text{A}-\text{B})\cos(\text{C}-\text{D})=0$

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Q 27Solve the Following Question.(5 Marks)5 Marks

$\text{If}\ \frac{\cos(\text{A}-\text{B})}{\cos(\text{A+B})}+\frac{\cos(\text{C+D})}{\cos(\text{C}-\text{D})}=0,$ prove that $\tan\text{A}\tan\text{B}\tan\text{C}\tan\text{D}=-1$

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Q 28Solve the Following Question.(5 Marks)5 Marks

$\text{If}\ \cos(\alpha+\beta)\sin(\gamma+\delta)=\cos(\alpha-\beta)\sin(\gamma-\delta),$
prove that $\cot\alpha\cot\beta\cot\gamma=\cot\delta$

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Transformation Formulae Maths - Transformation Formulae

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