Question

c) Evaluate the following:
3sin 370 5 cosec 399
Oos 530 sec 510
4 tan 230 tan 370 tan 670 tan 530
cos 17° cos 67° cosec 730 cosec 230​

Answer 1

Answer:

cosec39+32tan17tan38tan60tan52tan73−3(sin231+sin259)=0

Step-by-step explanation:

\begin{gathered}\frac{cosec39}{sec51}\\+\frac{2}{\sqrt{3}} tan17 tan38 tan60 tan52 tan73\\ - 3(sin^{2}31+sin^{2} 59)\end{gathered}sec51cosec39+32tan17tan38tan60tan52tan73−3(sin231+sin259)

\begin{gathered}=\frac{cosec(90-51)}{sec51}\\+\frac{2}{\sqrt{3}} (tan17 tan73) tan60 (tan38 tan52) \\- 3[sin^{2}(90-59)+sin^{2} 59]\end{gathered}=sec51cosec(90−51)+32(tan17tan73)tan60(tan38tan52)−3[sin2(90−59)+sin259]

\begin{gathered}=\frac{sec51}{sec51}\\+\frac{2}{\sqrt{3}} tan17 tan(90-17) \times \sqrt{3}\times tan38 tan(90-38)\\ - 3[cos^{2}59+sin^{2} 59]\end{gathered}=sec51sec51+32tan17tan(90−17)×3×tan38tan(90−38)−3[cos259+sin259]

=1+2\times (tan17 cot17) \times (tan38 cot38) - 3\times 1=1+2×(tan17cot17)×(tan38cot38)−3×1

=1+2\times 1\times 1-3=1+2×1×1−3

= 1+2-3=1+2−3

=0=0

Therefore,

\begin{gathered}\frac{cosec39}{sec51}\\+\frac{2}{\sqrt{3}} tan17 tan38 tan60 tan52 tan73 \\- 3(sin^{2}31+sin^{2} 59) = 0\end{gathered}sec51cosec39+32tan17tan38tan60tan52tan73−3(sin231+sin259)=0

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