Advertisements
Advertisements
प्रश्न
Prove that `(sin θ + cosec θ)^2 + (cos θ + sec θ)^2 = 7 + tan^2 θ + cot^2 θ`.
उत्तर
L.H.S = `(sin θ + cosec θ)^2 + (cos θ + sec θ)^2`
=`(sin^2 θ + cosec^2 θ + 2 sin θ cosec θ + cos^2 θ + sec^2 θ + 2 cos θ sec θ)`
=`(sin^2 θ +cos^2 θ) + (cosec^2 θ + sec^2 θ) + 2sin θ (1/sin θ) + 2 cos θ (1/cos θ)`
= `(1) + (1 + cot^2 θ + 1 + tan^2 θ) + (2) + (2)`
= `7 + tan^2 θ + cot^2 θ`
= R .H. S
APPEARS IN
संबंधित प्रश्न
From a point O in the interior of a ∆ABC, perpendicular OD, OE and OF are drawn to the sides BC, CA and AB respectively. Prove
that :
`(i) AF^2 + BD^2 + CE^2 = OA^2 + OB^2 + OC^2 – OD^2 – OE^2 – OF^2`
`(ii) AF^2 + BD^2 + CE^2 = AE^2 + CD^2 + BF^2`
D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that AE2 + BD2 = AB2 + DE2
The diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter.
Find the length of the hypotenuse of a right angled triangle if remaining sides are 9 cm and 12 cm.
The given figure shows a quadrilateral ABCD in which AD = 13 cm, DC = 12 cm, BC = 3 cm and ∠ABD = ∠BCD = 90o. Calculate the length of AB.
AD is drawn perpendicular to base BC of an equilateral triangle ABC. Given BC = 10 cm, find the length of AD, correct to 1 place of decimal.
In triangle ABC, ∠B = 90o and D is the mid-point of BC.
Prove that: AC2 = AD2 + 3CD2.
Find the value of (sin2 33 + sin2 57°)
In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AC2 - AB2 = 2BC x ED
If ΔABC ~ ΔPQR, `("ar" triangle "ABC")/("ar" triangle "PQR") = 9/4` and AB = 18 cm, then the length of PQ is ______.
