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3 years ago

Find the number of triangles with c =7, b=11, and B=21 degrees

Mathematics

1 answer:

muminat3 years ago

6 0

<h3>Answer:</h3>

<h3>Step-by-step explanation:</h3>

The given angle is opposite the longest given side, so there will be exactly one solution.

_____

The number of solutions may be 0, 1, or 2 when the given angle is opposite the shortest given side.

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3 years ago

Prove the following identity sin x(sec x+cscx)= tan x +1

Alexxandr [17]

Answer:

Step-by-step explanation:

________________________________________________________

FACTS TO KNOW BEFORE SOLVING :-

$\sin x = \frac{1}{cosec \: x} \: \: or \: \: cosex \: x = \frac{1}{\sin x}$

$\cos x = \frac{1}{\sec x} \: \:or \: \: \sec x = \frac{1}{\cos x}$

$\tan x = \frac{\sin x}{\cos x}$

________________________________________________________

In the question ,

L.H.S. = $\sin x (\sec x + cosec \: x)$

R.H.S. = $\tan x + 1$

Lets solve L.H.S. first.

$\sin x (\sec x + cosec \: x)$

$=> \sin x( \frac{1}{\cos x} + \frac{1}{\sin x} )$

$=> \frac{\sin x}{\cos x} + \frac{\sin x}{\sin x}$

$=> \tan x + 1$

∴ L.H.S. = R.H.S. (Proved)

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3 years ago