Question

Tan teta=7/24 find sin teta + cos teta

Answer 1

Answer:

$tanθ = \frac{7}{24}$

Hypotenuse = 7² + 24² = 49 + 576 = 625 = 25²

$tanθ = \frac{opposite}{adjacent}$

So Adjacent = 24 and Opposite = 7

$sin θ= \frac{opp}{hypotenuse} = \frac{7}{25}$

$cosθ = \frac{adj}{hypotenuse} = \frac{24}{25}$

$sinθ + cosθ = \frac{7}{25} + \frac{24}{25} = \frac{31}{25} = 1 \frac{6}{25}$

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Answer 2

Given,

$tan\theta=\frac{7}{24}$

We have to find the value of $sin\theta+cos\theta$

We know that

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

Here,

$tan \theta = \frac{7}{24}$

So,

$sin\theta = 7$

$cos\theta=24$

According to the question,

$sin\theta+cos\theta=7+24$

$= 31$

Therefore, the value of $sin\theta+cos\theta$ is $31$.