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DIBYARANJAN PRADHAN

· started a discussion

· 1 Months ago

gtt (Question:113008.0)

gt

Question:
If \(sin\ \theta=\cfrac{8}{17}\), where  \(0^o<\theta<90^o\), then \(tan\ \theta+sec\ \theta\) is:
Options:
A) \(\cfrac{1}{3}\)
B) \(\cfrac{2}{3}\)
C) \(\cfrac{4}{3}\)
D) \(\cfrac{5}{3}\)
Solution:

Ans: (d)

Using pythagorus theorem


AC2 = AB2 + BC2

(17)2 = AB2 + (8)2

AB2 = 289 - 64

AB = \(\sqrt{225}\) .

AB = 15

\(\therefore\) \(tan\ \theta= \cfrac{8}{15}\) and \(sec\ \theta= \cfrac{17}{15}\).


 \(\therefore\)\(tan\ \theta\ +\ sec\ \theta= \cfrac{8}{15}+\cfrac{17}{15}=\cfrac{25}{15}=\cfrac{5}{3}\)

Knowledge Expert

· commented

· 1 Months ago

Dear student,
Please specify your doubt.
Keep learning,
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