Evaluate: Sin600 Cos300 + Cos600 Sin300 - Mathematics


sin600 cos300 + cos600 sin300



On substituting the values of various T-ratios, we get:
sin600 cos300 + cos600 sin300

=`(sqrt(3)/2 xxsqrt(3)/2 + 1/2 xx1/2 ) = (3/4 + 1/4 )=4/4 =1`

  Is there an error in this question or solution?
Chapter 6: T-Ratios of some particular angles - Exercises


RS Aggarwal Secondary School Class 10 Maths
Chapter 6 T-Ratios of some particular angles
Exercises | Q 1


if `sec theta = 5/4` find the value of `(sin theta - 2 cos theta)/(tan theta - cot theta)`

If sec 2A = cosec (A – 42°) where 2A is an acute angle. Find the value of A.

If sin θ ,` sqrt (3)/2` find the value of all T- ratios of θ .

If tan `theta = a/b`, show that `((a sin theta - b cos theta))/((a sin theta + bcos theta))= ((a^2-b^2))/(a^2+b^2)`

If sec `theta = 17/8 ` verify that `((3-4sin^2theta)/(4 cos^2theta -3))=((3-tan^2theta)/(1-tan^2theta))`

In the adjoining figure, `∠B  = 90° , ∠BAC = theta° , BC = CD = 4cm and AD = 10 cm`. find  (i)  sin theta and (ii) `costheta`

In a ΔABC , ∠B = 90° , AB = 12 cm and BC = 5 cm Find
(i) cos A (ii) cosec A (iii) cos C (iv) cosec C


`cot^2 30^0-2cos^2 30^0-3/4 sec^2 45^0 +1/4 cosec^2 30^0`

If A = 30, verify that:

(ii) cos 2A = `(1- tan^2A)/(1+tan^2A)`

In the following table, a ratio is given in each column. Find the remaining two ratios in the column and complete the table.

sin θ    `11/61`   `1/2`       `3/5`  
cos θ `35/37`       `1/sqrt3`        
tan θ     `1`     `21/20` `8/15`   `1/(2sqrt2)`

`(cos 28°)/(sin 62°)` = ?

sin20°   =  cos ______°

tan 30° × tan ______°  = 1

cos 40° = sin ______°

Given: cos A = `( 5 )/ ( 13 )`

Evaluate: (i) `(sin "A "–cot "A") / (2 tan "A")`

                (ii) `cot "A" + 1/cos"A"`

Given: sin θ = `p/q`.
Find cos θ + sin θ in terms of p and q.

Using the measurements given in the following figure:
(i) Find the value of sin θ and tan θ.
(ii) Write an expression for AD in terms of θ

If sin A = cos A, find the value of 2 tan2A - 2 sec2 A + 5.

In each of the following, one trigonometric ratio is given. Find the values of the other trigonometric.

cotA = `(1)/(11)`

In ΔABC, ∠A = 90°. If AB = 5 units and AC = 12 units, find: cos C

In the given figure, PQR is a triangle, in which QS ⊥ PR, QS = 3 cm, PS = 4 cm and QR = 12 cm, find the value of: sin P

In a right-angled triangle PQR, ∠PQR = 90°, QS ⊥ PR and tan R =`(5)/(12)`, find the value of sin ∠PQS

In the given figure, ΔABC is right angled at B.AD divides BC in the ratio 1 : 2. Find
(i) `("tan"∠"BAC")/("tan"∠"BAD")` (ii) `("cot"∠"BAC")/("cot"∠"BAD")`

In the given figure, AC = 13cm, BC = 12 cm and ∠B = 90°. Without using tables, find the values of: `("cos A" - "sin A")/("cos A" + "sin A")`

From the given figure, find all the trigonometric ratios of angle B

From the given figure, find the values of sin B

From the given figure, find the values of cot B

From the given figure, find the values of cos C

From the given figure, find the values of tan C

From the given figure, find the values of cosec C

If cos A = `3/5`, then find the value of `(sin"A" - cos"A")/(2tan"A")`

If sin θ = `"a"/sqrt("a"^2 + "b"^2)`, then show that b sin θ = a cos θ

From the given figure, prove that θ + ∅ = 90°. Also prove that there are two other right angled triangles. Find sin α, cos β and tan ∅

A boy standing at a point O finds his kite flying at a point P with distance OP = 25 m. It is at a height of 5 m from the ground. When the thread is extended by 10 m from P, it reaches a point Q. What will be the height QN of the kite from the ground? (use trigonometric ratios)

Statement A (Assertion): For 0 < θ ≤ 90°, cosec θ – cot θ and cosec θ + cot θ are reciprocal of each other.

Statement R (Reason): cosec2 θ – cot2 θ = 1


      Forgot password?
Use app×