Question

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Trigonometry!!!

●Find the value of cos 75°?​
●Find the value of sin 135° ?​
●$= \frac{ { \sin }^{2}48 }{ { \cos }^{2}48 } + 1 = ?$

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Answer 1

Answer:

Step-by-step explanation:

You can write cos 75= cos (45+30)

Now cos (a+b)= cos a*cos b-sin a* sin b

So,

cos (45+30)=cos 45*cos 30- sin 45* sin 30

You know the value of cos45 sin45 cos 30 and sin 30

So cos (45+30)={(1/sqrt 2)*(sqrt 3/2)-(1/sqrt 2)* 1/2)}

Solving that you will get

sqrt 3 - 1/2*sqrt 2

sin(135)

= sin (90 + 45) // sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

= sin(90)cos(45) + cos(90)sin(45)

= ( 1 x 1/√2) + (0 x 1/√2)

= 1/√2

= (√2)/2

Answer 2

Step-by-step explanation:

(1) Cos75°

Cos(45° + 30°)

Cos45° Cos30° - Sin45° Sin30°

(1/√2)*(√3/2) - (1/√2)*(1/2)

√3/(2√2) - 1/(2√2)

(√3 - 1)/2√2

(2) Sin(135°)

Sin(180° - 45°)

Sin (π - 45°)

Sin45°

= 1/√2

(3) Sin²48°/Cos²48° + 1

tan²48° + 1

= Sec²48°