Question

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Answer 1

Answer

$\sf\frac{31}{25}$

$\rule{200}2$

Explanation

We know that,

tan²∅ + 1 = sec²∅

Given, tan∅ = 24/7, so,

(24/7)² + 1 = sec²∅

→ sec²∅ = 576/49 + 1

→ sec²∅ = (576 + 49)/49

→ sec²∅ = 625/49

→ sec∅ = 25/7 (taking square root on both sides)

We know that, cos∅ = 1/sec∅

So, cos∅ = 7/25

Also, sin∅/cos∅ = tan∅

→ sin∅ = tan∅cos∅

→ sin∅ = 24/7 × 7/25

→ sin∅ = 24/25

Now, we know that for given ∅, sin∅ = 24/25 and cos∅ = 7/25

so, sin∅ + cos∅ = 24/25 + 7/25

→ sin∅ + cos∅ = 31/25.

Answer 2

Answer:

31/25

Step-by-step explanation:

consider theta as x since i can't find it's symbol .

then, tan x =p/b=24/7

Hence, p=24

and b=7

by Pythagoras theorem we have,

p square + b square = h square

hence, 24 square + 7 square=h square

h = 25

hence, sin x + cos x = p/h+ b/h

or. sin x +cos x= (p+b)/h

or. sin x+ cos x = (24+7)/25

or. sin x + cos x= 31/25

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