The value of the expression [(sin222°+sin268°)/(cos222°+cos268°)] +sin263° +cos 63°sin 27°
a. 3
b. 2
c. 1
d. 4
Solution:
We have to find the value of the expression [(sin²22°+sin²68°)/(cos²22°+cos²68°)] + sin²63° +cos63°sin27°
Using the trigonometric ratio of complementary angles,
sin (90° - A) = cos A
sin²68° = sin²(90° - 22°) = cos²22°
So, sin²68° = cos²22°
Now, sin²22° + sin²68° can be written as
= sin²22° + cos²22°
By using the trigonometric identities,
cos² A + sin² A = 1
So, sin²22° + cos²22° = 1
Using the trigonometric ratio of complementary angles,
cos (90° - A) = sin A
cos²22° = cos²(90°- 68°) = sin²68°
cos²22° + cos²68° can be written as
= sin²68° + cos²68°
= 1
So, (sin²22° + sin²68°)/(cos²22° + cos²68°) = 1/1 = 1
Now, cos63°sin27° can be simplified as
= cos 63° sin (90° - 63°)
= cos 63° cos 63°
= cos²63°
Now, sin²63° + cos63°sin27° can be written as
= sin²63° + cos²63°
= 1
[(sin²22°+ sin²68°)/(cos²22°+ cos²68°)] + sin²63° + cos63°sin27° = 1 + 1 = 2
Therefore, the value of the expression is 2.
✦ Try This: The value of the expression [(sin²45° + sin²90°)/(cos²27° + cos²63°)] + sin²60° + cos 60° sin 30°
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8
NCERT Exemplar Class 10 Maths Exercise 8.1 Problem 11
The value of the expression [(sin222°+sin268°)/(cos222°+cos268°)] +sin263° +cos 63°sin 27°. a. 3, b. 2, c. 1, d. 4
Summary:
The value of the expression [(sin²22°+sin²68°)/(cos²22°+cos²68°)] + sin²63° + cos 63° sin 27° is 2
☛ Related Questions:
visual curriculum