Home
Class 10
MATHS
Without using trigonometric table, evalu...

Without using trigonometric table, evaluate the following: `(cosec^2(90-theta)-tan^2theta)/(4(cos^2 48^@+cos^2 42^@))-(2tan^2 30^@ sec^2 52^@ sin^2 38^@)/(cosec^2 70^@-tan^2 20^@`

Text Solution

Verified by Experts

`("cosec"^(2)(90^(@)-theta)-tan^(2)theta)/(4(cos^(2)48^(@)+cos^(2)42^(@)))-(2tan^(2)30^(@)sec^(2)52^(@)sin^(2)38^(@))/(("cosec"^(2)70^(@)-tan^(2)20^(@)))`
`=(sec^(2)theta-tan^(2)theta)/(4{cos^(2)(90^(@)-42^(@))+cos^(2)42^(@)})-(2((1)/(sqrt(3)))^(2)sec^(2)(90^(@)-38^(@))sin^(2)38^(@))/("cosec"^(2)(90^(@)-20^(@))-tan^(2)20^(@))`
`=(1)/(4(sin^(2)42^(@)+cos^(2)42^(@)))-(2"cosec"^(2)38^(@)*sin^(2)38^(@))/(3{sec^(2)20^(@)-tan^(2)20^(@)})`
`=(1)/(4)-(2"cosec"^(2)38^(@)xx((1))/("cosec"^(2)38^(@)))/(3)=(1)/(4)-(2)/(3)=(-5)/(12)`
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO TRIGONOMETRY

    NAGEEN PRAKASHAN|Exercise Problems From NCERT/exemplar|29 Videos

  • INTRODUCTION TO TRIGONOMETRY

    NAGEEN PRAKASHAN|Exercise Exercise 8a|20 Videos

  • CONSTRUCTIONS

    NAGEEN PRAKASHAN|Exercise PROBLEMS FROM NCERT/ EXEMPLAR|10 Videos

  • LINEAR EQUATIONS IN TWO VARIABLES

    NAGEEN PRAKASHAN|Exercise Revision Exercise Long Answer Questions|8 Videos

Similar Questions

Explore conceptually related problems

Without using trigonometric table,evaluate the following: (cos ec^(2)(90-theta)-tan^(2)theta)/(4(cos^(2)48^(@)+cos^(2)42^(@)))-(2tan^(2)30^(@)sec^(2)52^(@)sin^(2)38^(@))/(cos ec^(2)70^(@)-tan^(2)20^(@))

Without using trigonometric tables , evaluate the following : (cot(90^(@)-theta)*sin(90^(@)-theta))/(sintheta)+(cot40^(@))/(tan50^(@))-(cos^(2)20+cos^(2)70^(@))

Write the value of "cosec"^(2)(90^(@)-theta)-tan^(2)theta.

Without using trigonometric tables, evaluate each of the following: (-tanthetacot(90^0-theta)+secthetacos e c(90^0-theta)+sin^2 35^0+sin^2 55^0)/(tan10^0tan20^0tan30^0tan70^0tan80^0)

Without using the trigonometric tables, evaluate the following : (11)/(7) (sin 70^(@))/(cos 20^(@)) - (4)/(7) (cos 53^(@) "cosec" 37^(@))/(tan 15^(@) tan 35^(@) tan 55^(@) tan 75^(@))

Without using trigonometric tables,find the value of the following expression: (sec(90-theta)*cos ec theta tan(90-theta)cot theta+cos^(2)25+cos^(2)65)/(3tan27^(@)*tan63^(@))

Without using trigonometric tables, evaluate : (i) cos 48^@-sin42^@ (ii) cosec31^@-sec59^@ (iii) cot 34^@-tan56^@ (iv) cos^2 13^@-sin^2 77^@

Without using trigonometric tables,evaluate each of the following: (sin^(2)20^(@)+sin^(2)70^(@))/(cos^(2)20^(0)+cos^(2)70^(@))+(sin(90^(@)-theta)sin theta)/(tan theta)+(cos(90^(@)-theta)cos theta)/(cot theta)+cos(40^(0)+theta)-sin(50^(@)-theta)+(cos^(2)40^(0)+cos^(2)50^(@))/(sin^(2)40^(0)+sin^(2)50^(@))

(tan(90^@-theta) cot theta)/(cosec^2 theta)-cos^2 theta=0

Without using trigonometrical tables; prove (sin theta)/(sin(90-theta))+(cos theta)/(cos(90^(@)-theta))=sec theta*cosec theta