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Answer:
x = 4/3 (improper frac) = 1 1/3 (mixed frac) = 1.33... (recurring non terminating decimal)
Step-by-step explanation:
I'll be using T for theta.
4sinT = 3
=> sin T = 3/4
so, cosec T = 4/3
now, base = root [16-9] = root(7)
hypotenuse = 4
perpendicular = 3
so, cot T = root(7)/3
sec T = 4/root(7)
cos T = root(7)/4
now, putting the values in the equation, we have,
root[(16/9 - 7/9)/(16/7 - 1)] + 2root(7)/3 = root(7)/x + root(7)/4
=> 3root(7)/3 - root(7)/4 = root(7)/x
dividing both sides by root(7),
=> 1 - 1/4 = 1/x
=> 1/x = 3/4
or, x = 4/3 = 1 1/3 = 1.33...
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