Question

sinx+siny+sinz+sinw=4 then sin^2020y+cos^2021z+cos2020w=​

Answer 1

Given : sin x + sin y + sin z + sin w = 4

To find : The value of sin²⁰²⁰y + cos²⁰²¹z + cos²⁰²⁰w

solution : It is very tricky question. you know values of sine and cosine always lie between-1 to 1.

i.e., -1 ≤ sinΦ ≤ 1

here it is given that

sin x + sin y + sin z + sin w = 4

it is possible only if sin x , sin y , sin z and sin w have maximum of their value.

i.e., sin x = sin y = sin z = sin w = 1

it means, x = 90° , y = 90° , z = 90° and w = 90°

now you can easily find the value of sin²⁰²⁰y + cos²⁰²¹z + cos²⁰²⁰w

= (1)²⁰²⁰ + (0)²⁰²¹ + (0)²⁰²⁰

= 1 + 0 + 0 = 1

Therefore the value of sin²⁰²⁰y + cos²⁰²¹z + cos²⁰²⁰w = 1