Question

calculate the value of sin 105+cos 105

Answer 1

value is the 1/√2
hope it helps u

Answer 2

Step-by-step explanation:

Sin (105°) + Cos (105°)

Sin (105°) = Sin (60° + 45°)

∴Sin ( A + B) = SinA . CosB - CosA . SinB

Use the formula

Sin (60°+ 45°) = Sin60° . Cos45° - Cos60° . Sin45°

                      = √3/2 . 1/√2 - 1/2 . 1/√2

                      = √3/2√2 - 1/2√2

Sin (105°)        = √3 -1/2√2

Now, Cos (105°)

Cos (A + B) = CosA . CosB - SinA . SinB

Cos (105°) = Cos (60° + 45°) = Cos60° . Cos45° - Sin60° . Sin45°

                                              = 1/2 / 1/√2 - √3/2 . 1/√2

                                              = 1/2√2 - √3/2√2

                            Cos (105°) = 1 - √3/2√2

∴Sin (105°) + Cos (105°)

= √3 - 1/2√2 + 1 -√3/2√2

= √3 - 1 + 1 - √3/ 2√2

= 1/2√2

∴Sin (105°) + Cos (105°) = 1/2√2

This is the required answer