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Which one of the following when simplified is not equal to one

Question

Which one of the following when simplified is not equal to one?

A

tan 1 8^{\circ} \times tan 3 6^{\circ} \times tan 5 4^{\circ} \times tan 7 2^{\circ}

B

sin^{2} 1 9^{\circ} + sin^{2} 7 1^{\circ}

C

\frac{2 sin 6 2 ^{\circ}}{cos 2 8 ^{\circ}} - \frac{sec 4 2 ^{\circ}}{cosec 4 8 ^{\circ}}

D

None of these

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Text solutionVerified

(1)

tan 1 8^{\circ} \times tan 3 6^{\circ} \times tan 5 4^{\circ} \times tan 7 2^{\circ}

=

tan 1 8^{\circ} \times tan (90 - 54)^{\circ} \times tan 5 4^{\circ} \times tan (90 - 18)^{\circ}

=

tan 1 8^{\circ} \times cot 5 4^{\circ} \times tan 5 4^{\circ} \times cot 1 8^{\circ}

=

1

(2)

sin^{2} 1 9^{\circ} + sin^{2} 7 1^{\circ}

=

sin^{2} 1 9^{\circ} + sin^{2} (90 - 19)^{\circ}

=

sin^{2} 1 9^{\circ} + cos^{2} 1 9^{\circ}

=

1

(3)

\frac{2 sin 6 2 ^{\circ}}{cos 2 8 ^{\circ}} - \frac{sec 4 2 ^{\circ}}{cosec 4 8 ^{\circ}}

=

\frac{2 sin 6 2 ^{\circ}}{cos ( 90 - 62 ) ^{\circ}} - \frac{sec 4 2 ^{\circ}}{cosec ( 90 - 42 ) ^{\circ}}

=

\frac{2 sin 6 2 ^{\circ}}{sin 6 2 ^{\circ}} - \frac{sec 4 2 ^{\circ}}{sec 4 2 ^{\circ}}

=

2 - 1

=

1

Thus, all are equal to one. Hence, none of these is the answer.

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Question Text	Which one of the following when simplified is not equal to one?
Answer Type	Text solution:1
Upvotes	150