Math, asked by shalini683, 1 year ago

If 5 cos theta - 4=0 then find : (a) sin theta (b) tan theta (c) sec theta + cosec theta




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Answers

Answered by TheMist
60

Answer :

 \large \sf a) Sin\theta = \frac{3}{5} \\ \\ \large \sf b) tan\theta = \frac{3}{4} \\ \\ \large \sf Sec\theta + Cosec\theta = \frac{35}{12}

Solution :

Given :

5 cos\theta - 4 = 0

To Find :

  \sf a) Sin\theta

  \sf b) tan\theta

  \sf c) Sec\theta + Cosec \theta

Some common Points :

  • \sf Sin\theta = \frac{P}{H}

  • \sf Cos\theta = \frac{B}{H}

  • \sf tan\theta = \frac{P}{B}

  • \sf Sec\theta = \frac{H}{P}

  • \sf Cosec\theta = \frac{H}{B}

  • \sf Cot\theta = \frac{B}{P}

where,

  • P = perpendicular
  • H = hypotenuse
  • B = base

Let's solve,

5 cos\theta - 4 = 0 \\ \implies \sf Cos\theta = \frac{4}{5}

we know,

\sf \cos\theta = \frac{B}{H}

So,

Base = 4

Hypotheses = 5

Perpendicular = ?

Firstly we have to find perpendicular,

By Pythagoras theorem ,

H²= B² + P²

\implies \sf 5^2 = 4^2 + P^2 \\ \implies\sf 25 = 16 + P^2 \\ \implies \sf p^2 = 9 \\ \implies \sf \boxed{\mathfrak{ p = 3}}

A) sinθ

\implies = \frac{p}{h}

\implies = \frac{3}{5}

b) Cosθ

\implies = \frac{b}{h}

\implies = \frac{4}{5}

c) Secθ + cosecθ

 \sf \implies  \frac{h}{b} + \frac{h}{p} \\ \\ \sf \implies  \frac{5}{4} + \frac{5}{3} \\ \implies \frac{20+15}{12} \\ \sf \implies \frac{35}{12}


sriyaaaa2004: same here
Answered by sriyaaaa2004
12
hey mate!!!!!! here you go...
Attachments:

sriyaaaa2004: I hope its correct
TheMist: mark me brain list please
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