Answer
Verified
385.8k+ views
Hint:This is related to trigonometric ratios of complementary angles; two angles are said to be complementary if their sums equals $90$ degrees. So just convert it to the same trigonometric functions, hence we can substitute their angles as the same.
Complete step-by-step answer:
As we know that $\cos ec(90 - x) = \sec x$
From the left hand side we get $\sec 4A$ as $\cos ec(90 - 4A)$ , hence substitute $\sec 4A$ with $\cos ec(90 - 4A)$ .
$ \Rightarrow \cos ec(90 - 4A) = \cos ec(A - {20^ \circ })$
As both left-hand side and right-hand side is in terms of $\cos ec$ , hence we can equate their angles as equal.
$ \Rightarrow 90 - 4A = A - 20$
By rearranging the terms, we get,
$ \Rightarrow 90 + 20 = 4A + A$
Perform the arithmetic operation,
$ \Rightarrow 110 = 5A$
Again, rearranging the terms, we get,
$ \Rightarrow 5A = 110$
$ \Rightarrow A = \dfrac{{110}}{5}$
Hence $A = 22$
Therefore,
The value of $A$ is $A = 22$ degrees.
Additional Information:The trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. ... The most widely used trigonometric functions are the sine, the cosine, and the tangent.
The complementary angles are the set of two angles such that their sum is equal to ${90^ \circ }$ . For example, ${30^ \circ }$ and ${60^ \circ }$ are complementary to each other as their sum is equal to ${90^ \circ }$ .
$\sin $ of an angle $ = $ $\cos $ of its complementary angle.
Thus, the measure of the acute angle $A$ can be easily calculated by making use of trigonometry ratio of complementary angles.
Note: We have to check whether the given question is related to trigonometric ratios of complementary angles, then their angles must be in complementary which means that we can write their angles sum equals $90$ degrees.
Complete step-by-step answer:
As we know that $\cos ec(90 - x) = \sec x$
From the left hand side we get $\sec 4A$ as $\cos ec(90 - 4A)$ , hence substitute $\sec 4A$ with $\cos ec(90 - 4A)$ .
$ \Rightarrow \cos ec(90 - 4A) = \cos ec(A - {20^ \circ })$
As both left-hand side and right-hand side is in terms of $\cos ec$ , hence we can equate their angles as equal.
$ \Rightarrow 90 - 4A = A - 20$
By rearranging the terms, we get,
$ \Rightarrow 90 + 20 = 4A + A$
Perform the arithmetic operation,
$ \Rightarrow 110 = 5A$
Again, rearranging the terms, we get,
$ \Rightarrow 5A = 110$
$ \Rightarrow A = \dfrac{{110}}{5}$
Hence $A = 22$
Therefore,
The value of $A$ is $A = 22$ degrees.
Additional Information:The trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. ... The most widely used trigonometric functions are the sine, the cosine, and the tangent.
The complementary angles are the set of two angles such that their sum is equal to ${90^ \circ }$ . For example, ${30^ \circ }$ and ${60^ \circ }$ are complementary to each other as their sum is equal to ${90^ \circ }$ .
$\sin $ of an angle $ = $ $\cos $ of its complementary angle.
Thus, the measure of the acute angle $A$ can be easily calculated by making use of trigonometry ratio of complementary angles.
Note: We have to check whether the given question is related to trigonometric ratios of complementary angles, then their angles must be in complementary which means that we can write their angles sum equals $90$ degrees.
Recently Updated Pages
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
What are the possible quantum number for the last outermost class 11 chemistry CBSE
Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Select the correct plural noun from the given singular class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
The sum of three consecutive multiples of 11 is 363 class 7 maths CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
How many squares are there in a chess board A 1296 class 11 maths CBSE