# Recent questions tagged trigonometry-and-its-applications

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### The angle of elevation of a cloud from a point h meter above a lake is $\theta$. The angle of of depression of the lake is $45^{\circ}4. The height of the cloud is ### The captain of an aeroplane who is flying at an attitude of$1200\;m$sights two ships at an angle of depression of$60^{\circ}$and$30^{\circ}$. The distance between the two ships is ________ ### From the top of a$50\;m$high building , the angle of depression of a car on the road is$30^{\circ}$. The distance between the car and the building is ________ ### The angle of elevation of a cloud from a point$60\;m$above a lake is$30^{\circ}$and the angle of depression of the lake of the cloud in the lake is$60^{\circ}$. The height of the cloud is ### A kite is flying attached to a thread which is$165\;m$long. The thread makes an angle of$30^{\circ}$with the ground. The height of the kite from the ground is ________ ### If$2 cosec^2 30^{\circ} + x \sin^2 60^{\circ}- \large\frac{3}{4} $$\tan^2 30 =10 then the value of x is ________ ### The value of \sin (70^{\circ}+ \theta) - \cos (20^{\circ}- \theta )=________ ### If A and B are angle and \sin A = \cos B, then A+B =______ ### If \sin \theta + \cos \theta =1  then \cos \theta - \sin \theta=______ ### If (\sec \theta + \tan \theta) =m and (\sec \theta - \tan \theta ) =n then mn  =______ ### If 3 \sin \theta +5 \cos \theta =5, then 5\sin \theta -3 \cos \theta =_____ ### If a \cos \theta- b \sin \theta =c then (a \cos \theta)=________ ### The value of (cosec^2 \theta -1) \tan ^2 \theta = _____ ### The value of  \sin ^2 32+ \sin ^2 58 is ________ ### If x= r \sin \theta \cos \phi , y = \sin \theta \sin \phi , and z= r \cos \theta , then ### If  a \cot \theta + b\; cosec \theta =p and b \cot \theta + a\; cosec \theta =q , then p^2-q^2= ### \cos ^4 A - \sin ^4 A = ### If \large\frac{\sin \theta}{1+\cos \theta}= ### If  6x = \sec \theta  and  \large\frac{6}{x}$$= \tan \theta $, then the value of$6 \bigg(x^2 - \large\frac{1}{x^2} \bigg)$is __________ ### If$\cos \theta = \large\frac{3}{4}$then the value of$9 \tan ^2 \theta +9 $is ______ ### If$ \sin \theta + \cos \theta = \sqrt 2 \cos (90^{\circ}- \theta)$then$\cot \theta $is ### If$ \cos \theta = \large\frac{2}{3}$, then$2 \sec^2 \theta+2 \tan ^2 \theta -7$is equal to ### If$x \tan 45^{\circ} \cos 60^{\circ} = \sin 60^{\circ} cot 60^{\circ}$, then x=_______ ### The value of$\cos ^{\circ} \cos 2^{\circ} \cos 3^{\circ}...... \cos 179^{\circ} \cos 180^{\circ}$### The value of$\theta$satisfying$\sqrt 3 \sin \theta =\cos \theta$is ________ ### If$\sec 3A= cos (A-26^{\circ})$where$3A$is an angle, then the value of A is ________ ### If$\sec 4A= cosec (A-20^{\circ})$where$4A$is an angle, then th value of A is ________ ### If$A,B,C$are the interior angles of a triangle$ABC$, then$\tan \bigg(\large\frac{B+C}{2} \bigg)$$=_____ ### The value of \tan 5^{\circ} \tan 25^{\circ} \tan 30^{\circ} \tan 65^{\circ} \tan 85^{\circ} is ### The value of \tan 1^{\circ} \tan 2^{\circ} \tan 3^{\circ}....... \tan 89^{\circ} is ________ ### In \Delta PQR , right angled at Q, PQ = 3 \;cm and PR= 6\;cm . Then the value of  \Delta P  and \Delta R is ________ ### If  \sin (A+B) =1 and \cos (A-B)= \large\frac{\sqrt 3}{2}, 0^{\circ}$$< (A+B) \leq 90^{\circ}, A > B $then the value of A and B is ________ ### The value of '$\theta$' if$3 \tan ^2 \theta -1 =0$is ### If$2 \cos 3 \theta =1$then the value of$\theta$is ________ ### The value of$ \large\frac{\cos 30^{\circ}+\sin 60^{\circ}}{1+ \cos 60^{\circ}+ \sin 30^{\circ}}$is _______ ### In a right angle triangle right angle at A, if$\tan C= \sqrt 3$, then the value of$\sin B \cos C + \cos B \sin C$is _______ ### If$8 \tan A = 15$then$\sin A - \cos A$is ___ ### If$ \tan \theta = \large\frac{20}{21}$, then the value of$\large\frac{1- \sin \theta + \cos \theta }{1+ \sin \theta + \cos \theta }\$ is _______

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