Question
Prove the following.
cot2θ - tan2θ = cosec2θ - sec2θ
cot2θ - tan2θ = cosec2θ - sec2θ
✓
Answer
Get the step-by-step solution for this question inside the Vidyadip app.
Get the answer in the appNeed a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
In figure 3.76, seg PQ is a diameter of a circle with centre O. R is any point on the circle. seg RS⊥seg PQ.
Prove that, SR is the geometric mean of PS and SQ. [That is, SR² = PS ×SQ]
Prove that, SR is the geometric mean of PS and SQ. [That is, SR² = PS ×SQ]
Prove the following trigonometric identities.
$(1+\tan^2\theta)(1-\sin\theta)(1+\sin\theta)=1$
→$(1+\tan^2\theta)(1-\sin\theta)(1+\sin\theta)=1$
Find the values of p for which the quadratic equation $(2p + 1)x^2 - (7p + 2)x + (7p - 3) = 0$ has real and equal roots.
→Base of a triangle is 9 and height is 5. Base of another triangle is 10 and height is 6. Find the ratio of areas of these triangles.
Solve the following quadratic equation by factorization.
$2 x ^2-2 x +\frac{1}{2}=0 $
→$2 x ^2-2 x +\frac{1}{2}=0 $
Determine the nature of roots for each of the quadratic equation.
$3 x^2-5 x+7=0$
→$3 x^2-5 x+7=0$
In the figure, PA and PB are tangents to the circle drawn from an external point P. CD is a third tangent touching the circle at Q. If PB = 10cm and CQ = 2cm, what is the length PC ?, if PB = 10cm, what is the perimeter of $\triangle\text{PCD}$?
→If $\triangle ABC \sim \triangle DEF$ such that the area of $\triangle ABC$ is $9 cm^2$ and the area of $\triangle D E F$ is $16 cm^2$. If $B C=2.1$ cm . Find length of EF.
→If $\sin^2\theta\cos^2\theta(1+\tan^2\theta)(1+\cos^2\theta)=\lambda,$ then find is the value of $\lambda$.
→Very-Short and Short-Answer Qustions:
If $5\tan\theta=4,$ write the value of $\frac{\big(\cos\theta-\sin\theta\big)}{\big(\cos\theta+\sin\theta\big)}.$
→If $5\tan\theta=4,$ write the value of $\frac{\big(\cos\theta-\sin\theta\big)}{\big(\cos\theta+\sin\theta\big)}.$